Negotiating mathematics postdoc salary when having an offer with higher salary
I think that there is a difference between University 1 wanting you, and having you because you come with an NSF. That makes a huge difference in whether you can leverage for a higher salary or not.

The fact that University 1 did not offer you their regular postdoc title sounds like a hint to me that they will probably not be up for negotiation. Though, it doesn't hurt to try.