A few years ago I had to make a saved game for someone with the same problem. He had a Geforce 2. I got the save using an old computer with a Matrox Mystique, which is a much older video card.
You could try reducing video and audio acceleration, but that didn't work for the other person.
You could also try playing it in XP using ScummVM http://www.scummvm.org/downloads.php
Curse of Monkey Island is supposed to be compatible with it.
Let me know if you want to go the saved game route. I (or someone else) would have to play past the problem area from your save, then return it to you. You'd need to make a save from right before peeling off the map.