Cut inner side of lip from teeth? Only you can fix this. The mouthpiece will always apply abt the same pressure against the edge of the teeth no matter which design...
Well what kind of inner rim edge does your Monette have? The other matter is if the rim is relatively flat. Even w/a well rounded inner rim the flat-ish rim contour can devastate the chops. Especially the upper lip of the receded jaw trumpet player.
Note carefully the rim contour of this Al Cass mouthpiece:
(oh crap I can't display the scan of typical Bach and Monette mouthpieces!!!)
The secret to Al Cass's success w/his mouthpieces was, in part the continuous radius edge.
You can bend your teeth backwards from undue arm pressure before you'll cut your lips.
Neither is a very good option though...