Dremel have a small diamond engraving tool shaped like a "T" - the flat top of the T is like a tiny grinding wheel. Perfect size to reach the post without touching the playfield...

With some care I was able to cut slots into the broken posts, and then unscrew them with a normal flat screwdriver.

Cheers
Jacob

Method I would be using, done this a few time before with success.

I would be careful drilling close to the existing broken screws. If the new thread bites into the broken screw then you will create more problems.