Have you tried penetrant?
The bolt, nut and washer method of getting a better grip could do the trick.
Careful use of heat can also help. I'll put some grease at cup and heat the cup until the grease wicks into the thread. I had to do just this on the removal of the NDS cup on a 50 year old Jack Taylor. Things can get pretty warm, like hot to the touch, well before and paint damage.