The Monty Hall problem has a simple resolution. At the beginning you had a 1/3 chance of picking the good door, and 2/3 chance of picking a bad door, meaning you probably picked a bad door at the start, so you should switch.
I also don't think changing the problem to an analogous one is as helpful as this direct and simple solution. Using 100 doors could mean multiple things. Maybe it means at the next stage you have 99 doors left. Maybe it means at the next stage you have 2 doors left. Why should I think either is the correct analog? You can just see the simple answer I've stated and be done with it.