I've been through this situation, trying to get the nut loose, so I can unscrew it and remove an old toilet seat to replace it. I ended up getting a hack saw, and getting underneath the screw head and sawing the screw in half, so the nut half falls away, and the screw can be lifted out. You might also want to try some WD-40 around the nut, then use a tight fitting wrench to start turning the screw. Hope this helps you out a bit.
Moe
Moe