I've had to get lock-nuts off spinning bolts/screws a fair number of times, and if their turning it can be a real ****!
One thing that I've started to do, that seems to work is to get some crazy glue, and put a couple of drops on the top of the bolt/screw to glue it to the top of the CP, once it sets, I either use my drill with a socket, and adjust the "Torque" setting to the minimum, or use a impact gun on the nut while also holding the screw head down. the multiple impacts help "nudge" the nut off a little each time until they just spin off, then a quick tap on the bolt with a hammer cracks the little bit of glue holding the head.
Just another idea, if that doesn't work, I second the Dremel tool.
sd