Question about jointly owned house after divorce

Here’s the scenario:

I’ve been trying to get the ED agreement signed for 9 months now. STBX does not have a lawyer and doesn’t plan to get one. I had a lawyer draw up the ED papers based on our mediation sessions. The only reason I want it signed is because I am buying STBX out for the marital home. Since we could not agree on a listing price, I had it appraised and I’m buying out half his equity in the agreement. The mortgage is in my name only whereas the deed is in both our names. The other portions of the agreement state that I will give him $X of my 401k through a QDRO and that I will pay him $X in alimony.

If he never signs the agreement and we get an absolute divorce, what happens regarding the house? At that point we would have no claim to ED, but could I be trapped in a property that we own jointly forever unless we can agree on a selling price?

Yes, and further, if you divorce without settling the issue of the house you will continue to own it jointly and he can institute and action for partition to obtain is share of the equity. It will not be based on a date of separation value at that time, but the current value.