How do I re-seat bridge posts??

Well how about this one then?

If your current approach fails get yourself a small piece of maple. Scrap will do. Whittle off some shavings using a pocket knife. Remove the tp or whatever you have in there and glue in the shavings around the hole, making the dimensions a little smaller. Use Titebond to glue it. That should be a much more permanent fix.
Good idea.

OR - simply bring it to a luthier. The fix will be cheaper than buying a Dremel and hoping you get it right.

I bet you read the manual too....

Usually AFTER I've broken something...