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You are 'barking up the wrong tree', as I already completely agreed with what you say here. Unrestricted drops have an enormous impact on the entire game.

But this was not the alternative I was proposing: I wanted to get rid of the drop/gating altogether, by simply putting the exo-piece in a fixed place in the opening array. If I try to look at (many of) your variants through the eyes of a normal Chess player, I perceive this concept of gating as the most important new feature, not the fact that there is a new piece type. Games where it was possible to gate in a piece I already knew, say an extra Bishop, would already scare me off. The reason is that this type of gating must occur early, or you run the risk of losing the right to introduce the piece. So it will be an alien element, complicating opening theory. Normal Chess players rely very much on opening theory, and the idea that they might easily give away the game by not handling the introduction of the exo-piece correctly, while they have no idea how it should be done, could be a severe deterrent.

This is much less of a problem when the exo-piece starts in a fixed location, which is the same for both sides.