I think that while hosting LMAD was a positive experience for Monty, I always got the impression he felt that his hosting typecasted him and he had problems finding roles where he could act and sing. In the documentary, Deal!, The Making of Let's Make a Deal, Monty talks about how some have described LMAD as being "about greed." This description obviously upset him, as he tersely explained that he felt LMAD was never about greed. Watching the show, some contestants were perfectly happy being offered no more than $500 for an unknown box or curtain. It would be highly unlikely they would play for the Big Deal, but that didn't matter to some.
In terms of Monty guest starring on TV shows, at least a few times he played a character, or "himself", but not as a game show host. He did The Odd Couple, once as the LMAD host, and another time as himself, but in that one he got to sing. He also played a dentist that used hypnosis to numb pain in That Girl!, and on The Love Boat, he played a character.