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What options are there for shaving them down or removing those lips? Thanks!
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Get a nice sharp blade (brand new razor or box cutter) and just dive in man. Be fearless, but not sloppy. Start whittling down in small increments because it is better to cut away too little and have to keep going than to cut too much and be screwed.
If you are worried about nicking the teeth, I suppose if you soak it in piping hot water, you may be able to pull the lips away from the jaw to work on them with more room, but that is more work than it is worth my opinion as you would then have to glue them back and risk them separating again over time. Just cut careful and it should be fine.