You can't have it both ways

Can't have what both ways?

Either the way I describe is equivalent to the original experiment, only one door missing as I arrive to switch my original choice, or it isn't equivalent. To me it actually is equivalent.

You've lost me - what do you mean be 'one door missing as I arrive to switch my choice' ? You're there the whole time. You choose one of three unknowns, which means you have one chance in three of having chosen the prize, and then one of the other unknowns is shown not to have a prize. You then decide whether to switch. The remaining unknown has one chance in two of having the prize, which makes it worth switching to from your one in three choice.

If you don't choose until after one of the unknowns has been shown not to have a prize, you then have a choice of two unknowns, one of which has a prize. Your chance of the prize is one in two, and doesn't change if you decide to switch.

If one want to define the mathematics on what doors that really is existent at the time I arrive you're putting a lot of weight on what exist, less on the mathematics being equivalent.

I don't know quite what maths you're referring to, but if the maths doesn't match what exists, i.e. reality, you've probably made a mathematical error.

As the situation is the exact same, except that instead of me standing there, watching him choose a door, I'm on my way to the game. You could imagine me seeing him on a television, or someone informing me per telephone. Otherwise it should be the exact same as it seems to me, although he remove the door he opened before I arrive.

If he removes a door that doesn't have a prize, there are two doors left, one of which has a prize. When you choose one of the two doors, you have a one in two chance of the prize.

If you now assume that the odds change because of the removal of a door that we both know to be wrong, then it seems to me that you also have to assume that 'kismet' steps in, to rearrange what's behind the two doors that's left, somehow?

The odds change because there are fewer choices. That's the point of the 100 door explanation. If there is one prize and a hundred doors, and you choose one door, you have one chance in a hundred of the prize. If all the other doors except one are shown not to have the prize, that one has a 99 in 100 chance of having the prize. If you switch, you're choosing a 99 in 100 chance over your original 1 in 100 chance.

I'm not quite sure where your difficulty lies, but a surprising number of people do find it confusing.