When tapping, cut for 1/4 turn, then back off half a turn to clear chips, turn forward 1/2 turn to get where you started, then cut 1/4 turn again etc.
You get in to a swing of it, forward 3/4, backward 1/2 turn.
Doing that I have never broken a tap, although everybody says it is just a matter of time until I do.
Absolutely use a punch to start it off, or it WILL wander.
supergluing the mount is also not a bad idea, use it as a drilling jig. Heat gun or hair dryer will break the superglue after.