Good questions. They keep us thinking about the relation between text and historical narrative, which I think is vital for the current renewal of theology.

The suggestion that the Gospels were written to correct the over-spiritualized Jesus of the communities that we see reflected in the epistles is interesting. But if that were the case, wouldn’t we expect to see more obvious anti-docetic polemic in the Gospels? Is the corrective bias really apparent? The (synoptic) Gospels certainly present a historical Jesus, but I don’t see any reason to think that this was done in conscious reaction to an anti-historical distortion. I would also question whether the human Christ is missing from Paul’s letters. He is not especially interested in the details of Jesus’ life, but he is very interested in the very human suffering of Jesus - not least because he believes that he has been called to imitate it.

If Luke was concerned to correct the presentation of Jesus in the Gentile world, wouldn’t he have made the historical Jesus more prominent in the various speeches in Acts?

Paul gives some indication of what he originally taught: eg., the abandonment of idols, the resurrection of Jesus, who would ‘come’ to deliver believers from the wrath of God (1 Thess. 1:9-10); Christ crucified (1 Cor. 2:2; Gal. 3:1); a story about Jesus death and resurrection (1 Cor. 15:1-6); the power of the Spirit (Gal. 3:2-5). These are in agreement with the Gospels but I’m not sure they exhibit direct dependence on the Gospel traditions. But questions like this require more careful analysis.

I would also suggest that there was not one uniform kerygma. On the one hand, we need to allow for the natural diversity of human communication in a complex environment. On the other, I don’t think the good news for Israel (in Palestine or in the diaspora) was the same as the good news proclaimed to the Gentile world. The word ‘Gospel’ does not define its own content: it is simply a message of good news, but what’s good news for me may not be particularly good news for you.