Wow is that ugly. I've never messed with one of those back covers, but if it is solid, you could drill a pilot hole and use a screw extractor. Probably easier to do TheImPgoD's suggestion though. Could drip some nut loosener around the edges too. Get a little graphite down in those threads with a few taps for vibration to help work it in.
I'd be happy to pay someone a bit to take a whack at it... No liability implied. I live in what is effectively a closet while my house is being remodeled. I don't really have space to unpack tools... and stuff. Any takers?