Xtians: How exactly would God proving his existence undermine free-will?

It would depend on what kind of proof was offered. If it were merely a proof that a supreme being existed with the rest left contingent, e.g. if it failed to imply any other religious position, that wouldn't seem to be a problem, but if a proof then led to the logically necessary conclusion that a particular spiritual path or none was the most or only appropriate, one, that would undermine free will. I personally think that that's not the only reason. I think it's also aesthetic, a bit like a painting with a strand of hair accidentally left stuck to it.