I found that the best way of removing the cardboard monster tokens from the bases is to use a small screwdriver and pry the plastic slightly apart at the end where the token is removed. This will create a slightly larger opening and remove enough friction that the cardboard token will slide out. This will not work if you glued your token in when you glued the monster.
I hope this helps preserve any original monster tokens you may have so you can play both editions of Mansions of Madness.
We decided after second playthrough that the bases are an abomination, and I have ordered the clear acrylic discs for rebasing.
The bases that hold the counters were an interesting innovation for the first edition, when the tokens were different - special attacks varied from mini to mini, and the token was used to mark the difference. In 2nd edition, the bases are unnecessary, since the tokens are identical, and can be set to the side for reference when needed.
IMO, including the abominable bases in 2nd Ed was just a lazy design choice, and an ugly one to boot. 2-3 monsters in a space and the beautiful tile art is completely obscured.