I seem to recall during my recent playthrough of Escape, that I found Monkey Island's portion of the game to feel .. I dunno, off, somehow. Like the puzzles and such didn't feel as natural or as flowing as the ones earlier in the game had. The rock-throwing puzzle, in particular, really grated my nerves as it was far too easy for me to blink at the wrong time and mess up. I can't keep time in my head, so I couldn't like.. wait 2 seconds, blink, and then be ready to spot when I need to chuck the next rock.
As for Monkey Kombat.. I seriously feel that Escape was intended to be played on the PS2, because that whole section just felt at home with the controller and you had that "cheat sheet" which recorded the moves and such. I agree the stuff with Herman felt a bit like a deus ex machina, but then so did his having a ship in MI1. If anything, it really didn't surprise me in MI4.
EDIT: On the topic of whether to play MI 1 and 2 in the original version, or the Special Edition version.. I have been playing games for a good 30 years now (or just about), and I say there's nothing wrong with playing the SE versions over the old versions. They're very faithful to the original ones but with updated graphics (instead of being all new games, like you'd get with a remake). Plus they have voice acting, which helps with the immersion, and you can always switch back to the old timey style in the middle of playing. At least you could on the Xbox 360 versions I have.
In fact, I had fun playing through them twice; one with the enhanced graphics, one without. It's just a shame that MI1 SE didn't allow for the voices to remain when you switched back to the traditional graphics.