Okay, so rear brake was working fine, I've swapped wheels and now it won't release. Am I missing something?

 

Are the spacers in right and are they lined up properly? Sounds like the caliper is off and jammed up.

 

The mount was binding against the mounting hardware on the rotor. Would countersinking my new rotor hurt anything? Old rotor is countersunk but won't mount on my new wheel

 

I'm thinking you just answered your own question here...Ya need the right parts, or be creative...but, it Must Line-up properly.

 

Think your gonna find that unless you have access to a machine shop counter sinking that rotor isn't gonna be so easy. For what they cost find the right rotor it'll be cheaper than the tools you'll burn up.