It's my understanding that if it's marital property (it is, right?) that it can go 1 of 3 ways.
1. He gives you your share of equity
2. You give him his share of equity
3. The house is sold and you split the equity
#1 and #2 would probably depend in the other spouse being able to get approval for a new mortgage in their name (or with a co-signer like a parent or someone I guess)? Could you actually afford to stay if you run the numbers?
I think as you said the other challenge can be the appraisal process. One party is benefited by a lower fair market value vs. the other. Each hiring an appraiser and splitting the difference is one way to negotiate that.
Sometimes #3 is the only way to go if you hit a stalemate.
Now...on to you.
What do YOU want to do? Do you really want this house? Let's pretend this is not a divorce thing, but that he just poofed and is magically sent to the end of the earth or something. Would you want to still live there? Is this your forever house?
Or is this a perfect time to think about what kind of housing you'd like to transition into? Tired of house maintenance and yard work? Want a basement this time around? One level? Closer to work?
I think that's more important in the end then what he "wants to do" and changes his mind about every other minute. What are you able to afford and what do you want to do with your housing going forward.
(I know it chaps to think of him still in the marital home - but you'll tap into your strength if that's the case and find a way to make it part of your new beginnings).