The answer to this question is now apparent: no one got it all right. Anglicans and Lutherans did preserve the greatest slice of Epistle and Gospel readings after Pentecost.
Here is my best guess as to what the actual connection of propers, collects and readings should be. The readings show Jesus as a teacher, a miracle worker, and a purveyor of parables. The theme is Trust in God by means of Life in the Spirit.
First, Trinity Sunday displaced the First Sunday after Pentecost but Lutherans and Anglicans preserved the traditional readings: Rev. iv. 1. (The Throne in Heaven) and St. John iii. 1. (Jesus and Nicodemus) -- which "kicks off" the following sequence. So, the list is of Sundays after Trinity (assuming, of course, that the preservation of the proper sequence ought best be accomplished by simply pushing the First Sunday after Pentecost onto the next Sunday -- and not to the next weekday, as in Trent):
Domine in tua: O Lord, I trust in your merciful love. My heart will rejoice in your salvation. I will sing to the Lord who has been bountiful with me.
Deus in te sperantium: O GOD, the strength of all those who put their trust in thee; Mercifully accept our prayers; and because, through the weakness of our mortal nature, we can do no good thing without thee, grant us the help of thy grace, that in keeping thy commandments we may please thee, both in will and deed; through Jesus Christ our Lord. Amen.
1 St. John iv. 7. (Love Comes from God)
St. Luke xvi. 19. (The Rich Man and Lazarus)
Factus est: The Lord became my protector, and He brought me forth into a large place: He saved me, because He was well pleased with me.
Sancti nominis tuis: O LORD, who never failest to help and govern those whom thou dost bring up in thy stedfast fear and love; Keep us, we beseech thee, under the protection of thy good providence, and make us to have a perpetual fear and love of thy holy Name; through Jesus Christ our Lord. Amen.
1 St. John iii. 13. (Love One Another)
St. Luke xiv. 16. (The Banquet)
Respice in me: Look Thou upon me, O Lord, and have mercy on me: for I am alone and poor. See my abjection and my labor; and forgive me all my sins, O my God.
Deprecationem nostram: O LORD, we beseech thee mercifully to hear us; and grant that we, to whom thou hast given an hearty desire to pray, may, by thy mighty aid, be defended and comforted in all dangers and adversities; through Jesus Christ our Lord. Amen.
1 St. Pet. v. 5. (Cast Your Cares on Him)
St. Luke xv. 1. (The Lost Sheep)
Dominus illuminatio: The Lord is my light and my salvation: whom shall I fear? The Lord is the protector of my life: of whom shall I be afraid? My enemies that trouble me have themselves been weakened and have fallen.
Protector in te sperantium: O GOD, the protector of all that trust in thee, without whom nothing is strong, nothing is holy; Increase and multiply upon us thy mercy; that, thou being our ruler and guide, we may so pass through things temporal, that we finally lose not the things eternal. Grant this, O heavenly Father, for Jesus Christ's sake our Lord. Amen.
Rom. viii. 18. (Future Glory)
St. Luke vi. 36. (Love your Enemies)
Exaudi Domine: Hear, O Lord, my voice with which I have cried to Thee: be Thou my helper, forsake me not, nor do Thou despise me, O God, my Savior
Da nobis … Domine: GRANT, O Lord, we beseech thee, that the course of this world may be so peaceably ordered by thy governance, that thy Church may joyfully serve thee in all godly quietness; through Jesus Christ our Lord. Amen.
1 St. Pet. iii. 8. (Turn from Evil)
St. Luke v. 1. (Jesus Calls His First Disciples)
Dominus fortitudo: The Lord is the strength of His people, and the protector of the salvation of His anointed: save, O Lord, Thy people, and bless Thine inheritance, and rule them for ever.
Deus qui diligentibus: O GOD, who hast prepared for those who love thee such good things as pass man's under standing; Pour into our hearts such love toward thee, that we, loving thee above all things, may obtain thy promises, which exceed all that we can desire; through Jesus Christ our Lord, Amen.
Rom. vi. 3. (Dead to Sin, Alive to God)
St. Matt. v. 20. (Jesus Fulfills the Law)
Omnes gentes: Clap your hands, all ye nations: shout unto God with the voice of joy.
Deus virtutum: LORD of all power and might, who art the author and giver of all good things; Graft in our hearts the love of thy Name, increase in us true religion, nourish us with all goodness, and of thy great mercy keep us in the same; through Jesus Christ our Lord. Amen.
Rom. vi. 19. (The Wages of Sin)
St. Mark viii. 1. (Feeding of the Four Thousand)
Suscepimus Deus: We have received Thy mercy, O God, in the midst of Thy temple; according to Thy Name, O God, so also is Thy praise unto the ends of the earth; Thy right hand is full of justice.
Deus cujus providentia: O GOD, whose never-failing providence ordereth all things both in heaven and earth; We humbly beseech thee to put away from us all hurtful things, and to give us those things which are profitable for us; through Jesus Christ our Lord. Amen.
Rom. viii. 12. (Heirs with Christ)
St. Matt. vii. 15. (A Tree and its Fruits)
Ecce Deus adiuvat: Behold God is my helper, and the Lord is the protector of my soul: turn back the evils upon my enemies, and cut them off in Thy truth, O Lord my protector.
Largire nobis: GRANT to us, Lord, we beseech thee, the spirit to think and do always such things as are right; that we, who cannot do any thing that is good without thee, may by thee be enabled to live according to thy will; through Jesus Christ our Lord. Amen.
1 Cor. x. 1. (Warnings from Israel’s Past)
St. Luke xvi. 1. (The Unrighteous Steward)
Cum clamarum: When I cried to the Lord He heard my voice, from them that draw near to me; and He humbled them, who is before all ages, and remains for ever: cast thy care upon the Lord, and He shall sustain thee.
Pateant aures: LET thy merciful ears, O Lord, be open to the prayers of thy humble servants; and, that they may obtain their petitions, make them to ask such things as shall please thee; through Jesus Christ our Lord. Amen.
1 Cor. xi. 1. (Roles in Worship)
St. Luke xix. 41. (Jesus Weeps over Jerusalem)
Deus in Loco: God in His holy place; God who maketh men of one mind to dwell in a house; He shall give power and strength to His people.
Deus qui omnipotentiam: O GOD, who declarest thy almighty power chiefly in showing mercy and pity; Mercifully grant unto us such a measure of thy grace, that we, running the way of thy commandments, may obtain thy gracious promises, and be made partakers of thy heavenly treasure; through Jesus Christ our Lord. Amen.
1 Cor. xv. 1. (The Resurrection of Christ)
St. Luke xviii. 9. (Pharisee and the Tax Collector)
Deus in adjutorium: Incline unto my aid, O God: O Lord, make haste to help me: let my enemies be confounded and ashamed, who seek my soul.
Omnipotens sempiterne Deus: ALMIGHTY and everlasting God, who art always more ready to hear than we to pray, and art wont to give more than either we desire or deserve; Pour down upon us the abundance of thy mercy; forgiving us those things whereof our conscience is afraid, and giving us those good things which we are not worthy to ask, but through the merits and mediation of Jesus Christ, thy Son, our Lord. Amen.
2 Cor. iii. 4. (Ministers of the New Covenant)
St. Mark vii. 31. (Jesus Heals a Deaf and Mute Man)
Respice Domine: Have regard, O Lord, to Thy covenant, and forsake not to the end the souls of Thy poor: arise, O Lord, and judge Thy cause, and forget not the voices of them that seek Thee.
Omnipotens et misericors: ALMIGHTY and merciful God, of whose only gift it cometh that thy faithful people do unto thee true and laudable service; Grant, we beseech thee, that we may so faithfully serve thee in this life, that we fail not finally to attain thy heavenly promises; through the merits of Jesus Christ our Lord. Amen.
Gal. iii. 16. (The Purpose of the Law)
St. Luke x. 23. (Good Samaritan)
Protector Noster: Behold, O God, our protector, and look on the face of Thy Christ; for better is one day in Thy courts above thousands.
Omnipotens sempiterne Deus: ALMIGHTY and everlasting God, give unto us the increase of faith, hope, and charity; and, that we may obtain that which thou dost promise, make us to love that which thou dost command; through Jesus Christ our Lord. Amen.
Gal. v. 16. (Living by the Spirit)
St. Luke xvii. 11. (Ten Lepers)
Inclina Domine: Bow down Thine ear, O Lord, to me and hear me: save Thy servant, O my God, that trusteth in Thee: have mercy on me, O Lord, for I have cried to Thee all day.
Custodi quaesumus: KEEP, we beseech thee, O Lord, thy Church with thy perpetual mercy; and, because the frailty of man without thee cannot but fall, keep us ever by thy help from all things hurtful, and lead us to all things profitable to our salvation; through Jesus Christ our Lord. Amen.
Gal. vi. 11. (Paul’s Final Warning)
St. Matt. vi. 24. (Lamp of the Body)
Misere Mihi Domine: Have mercy on me, O Lord, for I have cried to Thee all the day; for Thou, O Lord, art sweet and mild, and plenteous in mercy to all that call upon Thee.
Ecclesiam tuam: O LORD, we beseech thee, let thy continual pity cleanse and defend thy Church; and, because it cannot continue in safety without thy succour, preserve it evermore by thy help and goodness; through Jesus Christ our Lord. Amen.
Ephes. iii. 13. (The Mystery of the Gospel)
St. Luke vii. 11. (Widow of Nain)
Justus est Domine: Thou art just, O Lord, and Thy judgment is right; deal with Thy servant according to Thy mercy.
Tua nos … Domine: LORD, we pray thee that thy grace may always prevent and follow us, and make us continually to be given to all good works; through Jesus Christ our Lord. Amen.
Ephes. iv. 1. (Unity in the Body)
St. Luke xiv. 1. (Man with Dropsy)
Da Pacem Domine: Give peace, O Lord, to them that patiently wait for Thee, that Thy prophets may be found faithful: hear the prayers of Thy servant, and of Thy people Israel.
Da quaesumus Domine populo: LORD, we beseech thee, grant thy people grace to withstand the temptations of the world, the flesh, and the devil; and with pure hearts and minds to follow thee, the only God; through Jesus Christ our Lord. Amen.
1 Cor. i. 4. (Thanksgiving)
St. Matt. xxii. 34. (Summary of the Law)
Salus Populi: I am the salvation of the people, saith the Lord: in whatever tribulation they shall cry to Me, I will hear them; and I will be their Lord for ever.
Dirigat corda nostra: O GOD, forasmuch as without thee we are not able to please thee; Mercifully grant that thy Holy Spirit may in all things direct and rule our hearts; through Jesus Christ our Lord. Amen.
Ephes. iv. 17. (Living as Children of Light)
St. Matt. ix. 1. (A Paralytic)
Omnia Quae Fecisti: All that Thou hast done to us, O Lord, Thou hast done in true judgment: because we have sinned against Thee, and we have not obeyed Thy commandments: but give glory to Thy Name, and deal with us according to the multitude of Thy mercy.
Omnipotens et misericors Deus: O ALMIGHTY and most merciful God, of thy bountiful goodness keep us, we beseech thee, from all things that may hurt us; that we, being ready both in body and soul, may cheerfully accomplish those things which thou commandest; through Jesus Christ our Lord. Amen.
Ephes. v. 15. (Children of Light)
St. Matt. xxii. 1. (Wedding Feast)
In Voluntate Tua: All things are in Thy will, O Lord; and there is none that can resist Thy will: for Thou hast made all things, heaven and earth, and all things that are under the cope of heaven: Thou art Lord of all.
Largire quaesumus Domine: GRANT, we beseech thee, merciful Lord, to thy faithful people pardon and peace, that they may be cleansed from all their sins, and serve thee with a quiet mind; through Jesus Christ our Lord. Amen.
Ephes. vi. 10. (The Full Armor of God)
St. John iv. 46. (The Official’s Son)
Si Iniquitates Observaveris: If Thou shalt observe iniquities, O Lord, Lord, who shall endure it? for with Thee is propitiation, O God of Israel.
Familiam tuam: LORD, we beseech thee to keep thy household the Church in continual godliness; that through thy protection it may be free from all adversities, and devoutly given to serve thee in good works, to the glory of thy Name; through Jesus Christ our Lord. Amen.
Phil. i. 3. (Thanksgiving and Prayer)
St. Matt. xviii. 21. (The Unforgiving Servant)
Dicit Dominus: The Lord saith: I think thoughts of peace, and not of affliction: you shall call upon Me, and I will hear you; and I will bring back your captivity from all places.
Deus refugium: O GOD, our refuge and strength, who art the author of all godliness; Be ready, we beseech thee, to hear the devout prayers of thy Church; and grant that those things which we ask faithfully we may obtain effectually; through Jesus Christ our Lord. Amen.
Phil. iii. 17. (Citizenship in Heaven)
St. Matt. xxii. 15. (Render unto Caesar)