Sounds to me like we're talking about a vrey small screw, like a #4 or #6 and if you broke the head off, It's also safe to assume that it is pretty darn tight.

An extractor really isn't an option - it's too small

Punching it out could very easily do damage.

Just drill new holes next to its original position and install the plate with new screws - If you want to, you can grind off the old screw if it's protruding