In my experience, I'm offered funding through the all but dissertation phase, with of course a clear timeline to follow. If your professor is willing to work with you on such a schedule, that might be a good sign that you'll be funde through completion just not after a certain point. Sorry if that doesn't make sense - regardless, I really recommend going with the place most willing to fund you the most, because as mentioned, they're the ones who value you the most. Up to you of course! Choose what seems best.