Ehrman yes, Carrier no. Ehrman starts off OK, but ends up trying to claim every book in the NT is inauthentic. I prefer to work with a broader consensus, which is that we have 7 authentic letters from Paul, others that are probably not, though there are reasonable arguments about Colossians. I’m skeptical about authorship for all the non-Pauline letters
John’s are a special situation. Both the Gospel and the letters come from what looks like an ongoing Johannine tradition, but it’s not obvious that they actually claim to be written by the original disciple.
Ehrman’s problem is that he’s stuck on an early 20th Cent theory that Jesus is a failed apocalyptic preacher. I think it’s pretty clear that he mostly preached that the Kingdom was present immediately in him, with some future elements that I’m not sure the Gospels preserve with complete accuracy. This goes back to the intro to the NT that he wrote when he was still a Christian. My impression from reading it was that he wasn’t using current historical Jesus scholarship.
I’ve seen several new approaches that are more rigorous. Not Carrier's, but others. I haven’t seen any where the data is clear enough to support them. Generally I prefer to stick with middle of the road critical scholarship, people like James Dunn and the authors of commentaries in major series like the Anchor Bible or Hermeneia.
Yes, Carrier is not middle of the road. I don't think you have to go down the Jesus as myth road. However, I like the idea of trying to apply a more "decision theory" approach to the evidence than having people just focusing on their particular pet theory with the corresponding supporting evidence. Some of the scholars are definitely better as you indicate. However, an approach like Carriers would have the benefit of capturing the best of all scholarly aspects from particular elements of all the best scholarly ideas and schools. Carrier is definitely worth your time to read, although it sounds like you are well read and would not find his particular arguments too persuasive for a mythical Jesus.
Have you ever seen a good treatment that Jesus may have been a failed Jewish rebel/political leader and that the gospels were an attempt to put a good spin on him two generations after he died for those remaining in the movement who didn't know much about the details of the founder? Especially Gentile followers. This would be in line with elements of your idea of kingdom immediately present in Jesus and elements of Ehrman's failed apocalyptic preacher. The idea being that Jesus had:
1. Gone too far in his ministry, which which had become mainly political in opposition to Rome (or combination of political/apocalyptic through the idea of the Kingdom of god becoming immediately present), aroused the Romans and was crucified; (general reason for Roman crucifixion was political agitation, the story offered in the gospels for why he was crucified seems very implausible and is strongly doubted by scholarship today - at least in its redacted form)
2. Two of his followers were probably crucified with him (some have taken this being hinted at in John and other early documents). The stories blaming the Jewish are most likely fictional because they don't make sense in terms of Jewish customs and how the material is presented in the gospels
3. After his crucifixion, the sect went underground (as is implied anyway in the gospels and Acts) as not to arouse notice and further trouble with Rome rather than the Jews. There still could have been trouble with some mainstream Jewish religious leaders and people that aroused Paul's interest. Paul shows very little knowledge of the Jesus of the gospels (the person who was supposedly presented as an historical figure). Paul seems pretty consistent in his authentic letters that his conviction surrounding Jesus was mostly experiential. Paul's more mystical than historical Jesus definitely would have been difficult to reconcile with an earlier historical Jesus unless the letters of Paul were only selectively used - which again seems possible from evidence
4. The more anti-Semitic tone of the gospels as they evolved over time was because of: a) More and more the sect moved away from the Christian sect's Jewish roots, and b)Presenting a positive view of the Romans to stay as far away from the original political Christian sect background who followed Jesus against Rome, as possible c) Have a convenient scapegoat to blame a fictional version of Jesus death to Gentile Roman Citizens, especially around A.D. 70 when the earliest gospels were probably written, Rome was dealing with the height of Jewish problem in Palestine. Jews were not popular. So become Roman loving Christian Jews.
5. Jesus overall influence in history was very minor compared to people like John the Baptist and the Zealots. He was nothing more than a failed rebel/preacher who thought the kingdom of god had come through his ministry (that could have had certain apocalyptic elements) but was mainly rebellious and political in nature.
6. It is interesting that we really have no other written material besides the letters of Paul from A.D. 30 -50 or any material at all for Jesus' life from about 4 B.C. to A.D. 30, that may have shown Jesus anti-Roman stance. The gospels also go out of their way to seem friendly to Rome - this is not how Jews thought of Roman occupation at this time. Was it hidden, lost or destroyed because it would have been very dangerous for the sect, especially around A.D. 70 with the problems with the Jews? This would provide a sufficient reason to hide or destroy any information that existed. Also, perhaps Jesus and his followers were betrayed by Jewish leadership and so Judas I and Jewish leaders, represents in the gospels betrayal in general as many also doubt the existence of Judas. Much of the other Biblical information that was believed about Jesus (from OT prophesy) is just switched from a proto-typical Messiah who was moving towards becoming a political/military savior for the Jews who was also preaching elements of an apocalyptic message (similar originally to John the Baptist but became more politicized because of rapid popularity increase after John's death) to the suffering servant lamb of god portrayal in the gospels.