My instincts are that there was a historical person behind all the myths.
The synoptics resort to all sorts of mental gymnastics to reconcile the historical Jesus with the messiah of OT prophecy. Look at the convoluted geography of the birth narratives for example.
Matthew and Luke both want Jesus born in Bethlehem because of the traditions connected with David's city. One account has him start in Nazareth and invents a census to get the family to Nazareth and then back up north a few days after the birth. The other account has his family living in Bethlehem and fleeing up north - via Egypt of course - because of King Herod.
None of this would have been necessary if he was invented out of "whole cloth".
I will look into the Carrier v Ehrman debate though.