I think you'll get it out one way or another, but if you have to apply some heat to loosen that cup up, well, so be it. The fact that you're considering a repaint anyway gives you some latitude in that regard.
I've applied heat in a situation where a prior mechanic used red loctite and managed not to damage the paint. Of course, that frame did not have Italian paint on it, which is programmed to come off the bike as soon as it sees a bump in the road. The invention of quick release paint is one of the high marks of Italian cycling innovation, of course.