First, the goal to prove Jesus' existence or not is methodologically a black hole from my perspective.
Second, another quest for what we can know about Jesus will turn up nothing new, because each thing that will be identified will be easily deconstructed by the members of the group. When this happens, I can imagine that the minimal-to-nothing "evidence" could be framed as "proof" for Jesus' non-existence. The media will have a heyday - "now scholars prove that Jesus didn't exist" or "scholars say that we can know nothing about Jesus".
This line of reasoning became very evident to me when Tom Verenna quoted a statement of mine published on my blog (in which I stated that the historical Jesus we reconstruct only exists in our imaginations) as somehow aligning with his myther position, as giving validity to it. This is simply false. Because I recognize that my colleagues in the Jesus Seminar have constructed the historical Jesus from their imaginative interpretation of the evidence available, has no bearing on whether or not Jesus actually existed.
In fact, I think that Jesus did historically exist, although I cannot prove this anymore than the mythers can prove he didn't. I have reasons to think that he did exist, including the fact that Paul knew Jesus' brother James and that Hegesippus reports that he knew that the grandsons of Jesus' brother Jude had been interrogated under Domitian. And yes I know how mythers get around this evidence (how it is deconstructed), just as I know how Christians have traditionally gotten around it using some of the same arguments (since human brothers don't coincide with theologies like Mary's perpetual virginity, just as they don't coincide with the position that Jesus was not a historical person).
Unless there is a new orientation to the project, I will not be participating in it, and wish those who remain part of TJP my best.