Tannin, I think that we have all encountered your issue in the past. Those flat head screws can be a bear to remove and often get damaged beyond being able to use them again, or they get damaged when someone tries to tighten them too much with too small of a screwdriver. Either way, the slot gets mangled.
I stumbled across something that works really well with either removal or tightening. I use a hand impact wrench, the type that you hit with a hammer to make work. I took a 1/2" hex head bolt and ground it down so that it has a tip that is the thickness of the screw head slot. The hex head fits into a socket on the impact wrench. Using this device makes it easy to remove the screws (and save them!) and also allows good tightening when replacing.
Won't help you with your mangled screws, but might help you when installing new ones.
Matt