Ops, the other mount is for stick trans cars yours is an auto?

If all mounts are unbolted, there should be nothing else holding engine to sub frame. Perhaps the mount bolts are binding in their holes.

Try taking off the single nut/bolt on two front mounts and leave the rear trans mount nut on.

 

I tried to tap on the bolts with a hammer to see if they would move. The mount closest to the front moves fine, but the other two don't. In fact, a lot of rust debris falls when I tap them. Any chance something is fused?

I had another thought -- Since I have the car up on ramps, is the angle of pressure hindering me from jacking the engine straight up? Should I jack up the back of the car as well, put it on jack stands and try to jack up the engine again?

 

I would put the car on jack stands. Weight on the wheels puts pressure on the mounts of the engine and tranny.

 

If one mount moves, the others may be rusted to the chassis perhaps at the stud/hole area.

Hammering or prying may be your best bet. Find a nut(s) that can screw onto the stud threads to protect the threads. Then hit the nut head on with a hammer.

You could try penetrating fluid on stud/stud hole area. For best results wait overnight after applying.