I still haven't answered CJ's questions, but I'm working my way towards a post. Menawhile, I thought these seminal summarizing thoughts from F.F. Bruce, on the Gospel, were worthwhile as a starting point of reflection (though certainly not beyond improvement) regarding the shape of the NT teaching on the Gospel. Bruce says:

The NT use of Gk. euangelion, “joyful tidings,” “good news,” has an OT background in Is. 40-66, where the LXX verb euangelizomai, “bring good news,” is used of the declaration of Jerusalem’s deliverance from bondage (Is. 4:9; 52:7) and also of a wider announcement of liberation for the oppressed (Is. 61:1, 2). This last passage provided the text of Jesus’ inaugural preaching at Nazareth: he gave notice that it had been fulfilled as he spoke (Lk. 4:17-21). Jesus’ message was otherwise described as the gospel of the kingdom of God. Its contents are set out in his parables, where the Father’s loving bestowal of mercy and free forgiveness on the undeserving and the outcasts is presented with vividness and warmth.

With Jesus’ death and resurrection a new phase of the gospel begins. The preacher becomes the preached one: his followers, whom he commissioned to preach the gospel after his departure, proclaimed him as the one in whom the Father’s pardoning grace had drawn near. “The gospel of God. . . concerning his Son” (Rom. 1:1-3) tells how, in the coming and redemptive work of Christ, God has fulfilled his ancient promise of blessing for all nations.

For the first generation after Christ’s ascension the gospel was exclusively a spoken message; the earliest written record of the gospel appeared in the 60s.

Only one saving message is attested by the NT. The “gospel to the circumcision” preached by Peter and his colleagues did not differ in content from the “gospel to the uncircumcised” entrusted to Paul (Gal. 2:7), though the form of presentation might vary according to the audience. Paul’s testimony is, “Whether therefore it was I or they [Peter and his colleagues], so we preach, and so you believed” (1 Cor. 15:11).

The basic elements in the message were these: 1. the prophecies have been fulfilled and the new age inaugurated by the coming of Christ; 2. he was born into the family of David; 3. he died according to the Scriptures, to deliver his people from this evil age; 4. he was buried, and raised again the third day, according to the Scriptures; 5. he is exalted at God’s right hand as Son of God, Lord of living and dead; 6. he will come again, to judge the world and consummate his saving work.

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Two things strike me immediately: (1) first, the observation that "with Jesus’ death and resurrection a new phase of the gospel begins" is important, and perhaps overlooked in some current discussions; (2) the influence of C.H. Dodd on Bruce's summary has perhaps contributed to an underplaying of the Gospel's relation to the forgiveness of sin (unless you read the euphemistic "to deliver his people from this evil age" as sufficiently expressive of this emphatic NT point). Leon Morris supplies the corrective to this in "The Apostolic Preaching of the Cross."