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Just to add a few points, having gone through the same process with swapping pieces for a variant I'm working on:

• There is a difference between a piece swapping a pawn into promotion, and a pawn swapping with another piece into promotion. In the first case, it's intuitively the piece doing the swapping whose move it is and not the pawn's, so I don't promote the pawn, as it's not its move. In the second case, intuitively it's the pawn's move, so I follow the normal pawn promotion rules. If you don't want to make the above distinction between the two cases, you should make that clear in the rules, as intuitively a player will make the distinction.

• If you hold with the "not moved before" rules from normal chess, when introducing swapping moves, it can be very difficult to keep track of which pawns have or haven't already moved, as pawn's can reappear on their starting squares, or other pawns can end up on other pawns starting squares, so can get very confusing.

As an additional note: When introducing swapping moves into a variant, it can lead to too much change on the board when playing the game, removing any chance of strategical thinking, and limiting tactical thinking to only a few moves ahead. I'd try to limit the extent of the swapping rules, i.e. don't allow swapping with the royal (King) piece, and perhaps limit the swapping rules to only a handful of pieces.