I don't know what kind of mythicism Richard Carrier and the likes are dealing with these days, and how it fits into their construction of Paul (it's been years since I've kept up with what's going on there)... let me say that, like many of those people, I am also of a (full-blown) atheistic persuasion—but I always took issue with a lot of things they had to say. Oh, and it's incredibly late here, so sorry if this seems like just a list of items for research into Pauline/gospel community contacts.

In terms of very fundamental christological similarities between Paul and “other” traditions, 1 Cor 5:7 is quite significant, associating Jesus with the paschal lamb (and, perhaps also significantly, verse 8 warns against the "yeast of malice and evil" [see Mk 8:14, the "yeast of the Pharisees and the yeast of Herod"]).
Riesner (2003) really pushes for Paul's familiarity with a very early ransom logion (as in 1 Cor 9:19-23). I haven't read that paper in a long time, but I think he may overstate his case. Paper is "Back to the Historical Jesus Through Paul and His School (The Ransom Logion--Mark 10.45; Matthew 20.28)," in
JSHJ 2003.
1 Thessalonians 4:8 begs to be compared with Mk 9:37 || Mt 10:40 || Lk 10:16, with the Lukan version resembling it the most. Also, check out Kim, "The Jesus Tradition in 1 Thess 4.13-5.11," (
NTS 2002) for an argument that Paul had transmitted specific eschatological Jesus sayings to the Thessalonians (but had not properly understood them).
Tuckett (1983) did a study of the relationship between 1 Corinthians and Q material, concluding that “many of the alleged links show only a connection with part of the gospel tradition other than Q.” But he definitely concludes that sayings of Jesus “played some role at Corinth,” singling out 1 Cor 4:8 and 13:2 as the most clear-cut examples, and 7:10-11; 9:14; and 11:23-25 as also utilizing Jesus traditions.
I think Paul's “new temple” comments (in 1 Cor 3; 2 Cor 6) have affinities with other strands of early Christian tradition—especially check out the similarities in language between 2 Cor 5:1 and Mk 14:58.
David Sim has written a few papers recently on the anti-Pauline character of Matthew recently, but I think his arguments are pretty weak.
Martin Hengel on Luke: "[The author of Luke] respects Paul to the very highest degree as a divinely-guided missionary, charismatic, and church-planter, even though he partially distances himself from him theologically, under the influence of the Jerusalem tradition (which appears, for example, in the question of Paul's apostolic title) and its Jesus-tradition, which provided him with the impulse for his gospel."