Impossible movements: what's your suggestion?

I think it depends what kind of game you're making. If the position of the player and the things the player can see are important enough that they need to be preserved to prevent cheating or breaking the game, I would consider fading out the view if any part of the player's avatar is intersecting with geometry. I think the player will learn the limitations pretty quickly. You could probably take it one step further and black out the view if the player moves too far from their starting position (in the real world) even if it doesn't lead to intersecting.

In general, if the player is using a traditional control method to move their avatar around in the world, that should be the only thing that results in a permanent change in position in-game. Everything else should be treated like leaning (or stretching), to the extent that you allow it.

My feeling is that allowing a hybrid of traditional controls and actual body movement to move the avatar (aside from leaning) would only confuse and disorient the player anyway.

If you're using real-world body movement rather than traditional control methods to move the avatar, that changes things. I don't have any answers for that at the moment...