Here is the process I used for removing the post screws that broke off during removal of the posts. Unfortunately when they snap off, it is usually below the surface of the playfield. This makes it difficult. However the way i did it caused minimal damage which was hidden by the posts.
Mask around area to be drilled, in case drill slips and damages playfield.
Using a small drill bit, drill around post hole.
Tap broken screw side to side, back to front, to loosen up broken screw (Try not to do too much damage). Remember posts will hide any butchering. Grab the top of the screw with circlip pliers (Small and strong) and unscrew the broken piece of screw - Then toss it on the floor and swear at it.
Get a narrow piece of wood dowel, cut to length, drill out hole to same dimension as dowel.
Apply wood glue to dowel and hole, Insert dowel, wipe off excess glue and allow to dry.
Drill new hole in centre of dowel and screw in new post screw.