Dremel with either a properly-sized drill bit or round tip grinding bit will remove the mushroom. We careful not to overheat it (drill or grind awhile, and then let the pieces cool) or you will run the risk of melting plastic pieces in close proximity.
For re-assembly, I've been using some really small hex-head "bolts" that are designed for use in model railroading, and what I would attempt here (note I say "attempt") would be to drill a hole into the pin the size of the bolt shank, and then SuperGlue the bolt into the hole.
These are 00-90 x 1/18" by Woodlands (you should be able to find similar in your local hobby shop.
I used similar to repair the broken front suspension of a Classic Carlectables V8 Supercar Falcon.
