I notice two or three areas on the gun that appear black. I wonder if these are areas that have, or maybe had, roll makings, or stampings. That is, I wonder if the markings have all been ground off.
After the soaking, round toothpicks will help clear/clean out the screw slots. If any of the paint worked it's way into screw threads, it may take a long soaking time to free that up. A week or two would not be unreasonable.
When using heat, the idea is to heat the metal surrounding the screw, but not the screw itself. Heating the surrounding metal will cause the screw hole to expand, which ought to break a rust bond. When using cold, the idea is to cool only the screw, and not the surrounding area. This will cause the screw to shrink diametrically, again breaking the rust bond.
Mike Priwer