Don't forget that you have multiple axes to negotiate on: I would happily take a 25% pay cut if it came with a couple months worth of PTO. Then, when they're unwilling to budge on the PTO, you can leverage that back into getting the salary number moving again.

I find that kind of haggling to work best as a synchronous, ideally face-to-face, communication. In that setting, it's very unlikely that you can't manage to smooth over any too ambitious of an ask and arrive at some sort of agreeable number.