So two perceptive people who understand the calculations still disagree about various additional issues shows. That shows just how confusing the whole set-up really is.

Not necessarily quite that, I'd say. The original game had, as we all remember, just one player. When you involve a second player, there are a whole slew of ways you could do so, and many of these have different consequences:

i) you can assume the player arrives entirely after the whole game has played. He sees one closed door and two open ones. The open ones may show goats and/or a car.

ii) you can assume the player arrives entirely after the whole game has played. He sees one closed door and two open ones. The open ones are now both empty because the goat has wandered off and the car has been driven away.

ii) you can assume that the game delivers at most one car, so that gives different results whether the car has or has not already been won.

ii) you can assume that the game can deliver more than one car: whichever door the original person picked is closed again and a fresh goat or car is placed behind it, matching the original contents.

iii) you can assume the original player and the new player pick their doors at the same time with no knowledge of what the other picks, and if the pick the same door they have the job of deciding how to share the car or goat.

iv) you can assume the original player and the new player can only open one door each but they negotiate to decide who gets which door

....

and so on.

So the disagreements may simply be due to playing a different 'extended game'.