I use entities outside human experience in thought experiments for the sake of preventing Clever Humans from trying to game the analogy with their inferences.

"If Monty 'replaced' a grain of sand with a diamond then the diamond might be near the top, so I choose the first bucket."

"Monty wants to keep the diamond for himself, so if he's offering to trade with me, he probably thinks I have it and wants to get it back."

It might seem paradoxical, but using 'transmute at random' instead of 'replace', or 'Omega' instead of 'Monty Hall', actually simplifies the problem for me by establishing that all relevant facts to the problem have already been included. That never seems to happen in the real world, so the world of the analogy is usefully unreal.

At this point you've had this explained to you multiple times. May I suggest that if you don't get it at this point, maybe be a bit of an empiricist and write a computer program to repeat the game many times and see what fraction switching wins? Or if you don't have the skill to do that (in which case learning to program should be on your list of things to learn how to do. It is very helpful and forces certain forms of careful thinking) play the game out with a friend in real life.

The thing you might be overlooking is that Monty does not open a door at random, he opens a door guaranteed to contain a goat. When I first heard this problem, I didn't get it until that was explicitly pointed out to me.

If Monty opens a door at random (and the door could contain a car), then there is no causal link and therefore the probability would be as you describe.