Then the game launches just as normal and you can, for instance, just pass that area that was making the game crash (in my case, trying to enter Melee harbor after getting the painting), then save and continue from Steam just as normal.
If your game is installed (Steam installation should work just fine), just run that software and press 'Play Fullscreen'. This is completely safe (one of the few instances on the whole internet where someone actually doesn't want to take your money). The workaround I found is actually to download a very, very useful tool that an independent programmer made years ago, that specifically allows Escape from Monkey Island to run on modern operating systems. I tried carrying different objects, going fast and slow, etc.
There is no fix (or at least I haven't found it) within the game.
