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Charles, well hit. Truthfully, I never considered the question of pawn promotion when I finished this up for posting. Embarrassing to admit, but there it is. I kept going back to the game with the feeling that something was missing, but the taxi rules seemed solid, I had the combination and breakdown rules set, the dyads and triads had their possible moves trimmed down to what I thought worked best [the original had R+R movement options of 'hookrook' and planar rook, for example, but those moves were too powerful]. Good thing this is a non-competing entry, apparently.
My initial thoughts, way back when, were that there was no promotion, the pawns would have to be carried off the back row by a taxi or as part of a combination piece, or using the optional pawn moves I left in the rules, should the situation ever arise. This is clearly a weakness in a *chess* variant design. Following are promotion rules.
Promotion would occur on the opponent's 3-square back rank. 
To promote, a pawn must, by itself, move onto one of the 3 promotion squares. It may not promote if brought to a promotion square by taxi or as part of a combination piece.
A pawn may only promote to a rook, bishop, or knight. This is freely chosen, there are no restrictions on availability of pieces or any other such conditions.
I hope this is satisfactory.