Having recently replaced the hinges for a 1940s house, I think this might be the way.
I got the flat head screws out by cleaning the groove, putting a screw driver in, then smacking it with a hammer, hard. Then I unscrewed. It took a lot of time, and about 1/3rd the screws snapped in half (which was fairly helpful, as it got the hinge off).
The hammer is the key. Granted I'm not working on 1940s stuff so you have a unique challenge. Usually I am just dealing with painted over screws no older than 1970s, but usually just a good screwdriver and a hammer gets the job done for me.
And this is an important feature of slotted screws, it is much easier to get paint out of them than any other system. If the screws snap it is usually a case of bad screws rather than the system. The ultimate driver for slotted screws is a Stanley Yankee, and probably what put them in the first time!
