Using a topic as hideously contentious as the historicity of Jesus strikes me as a brilliant move - the scholars will know Carrier knows his stuff, the skepticsphere will trumpet the book far and wide, the churches will absolutely shit ... someone might even read the book in between denouncing it.

I'm not sure that will happen. Look through Carrier's blog for reviews of Proving History: by and large they look like statistical carping of the sort which will make people think 'ah, it's just scientism: arrogant application of tools of limited domain outside their correct area, and the math isn't even right, apparently'.

It's early days yet, of course, but in Google Scholar I see nothing citing '"Proving History" Carrier'.