According to a quick search on Google News, "to proselytize" is much preferred to "to proselyte." 66 to 2. But that doesn't mean I have to think it sounds good to say it.
I say proselyting. I think proselytizing sounds ridiculous. I have a pet peeve when people say that they're disorientated instead of disoriented, and my preference in this case seems like a corollary to that (even though I know they're not very similar in actuality). It's a personal thing, I guess.
Proselytize is the correct and original form; as was pointed out, a proselyte is a "new convert". People have used the term incorrectly, and hence to "proselyte" has come into existence, but it is the late comer, not the original.
