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After posting my previous comment on Grand Chess, I received an email from Michael Howe [Nova Chess and others], who has been working on the pawn promotion/movement problem in his work. With permission, I present the relevant body of the text: 
[A pawn] 'can move to the back rank even when no previously captured piece is available, and while there it moves like a nonroyal king (commoner).  If it moves out of the promotion zone it reverts to pawn.  If it moves within the promotion zone it gets another chance to promote.  A player can also move into or within the promotion zone and choose the commoner option instead of a piece promotion even if a piece is available: for example, in a situation when a commoner would mate but a cardinal or marshal would not.  No in-situ promotion.  I think this works better than a sideways-moving pawn because it is more threatening, although I doubt that this situation will come up much'.

As I use the scheme I proposed in both Grand Shatranj and Atlantean Barroom Shatranj, I am adding this option to both games.