Try a little shot of PB Blaster or WD40 to make sure the plungers pop all the way out when the door is open, and plunge them a few times.

The door switches are probably not bad. If you feel like pulling your kick panels you can figure out which one is shorting, and possibly even find where. Just reach in and find the harness, and jiggle the wires to see which one causes the dome light to go back off. Doors shut and bulb back in, naturally...