Its usually said that pawn double step rule is to make chess faster.
On normal chess, there are 6 squares between pawn and promotion, and with those 6 squares between them, the double step rule is needed.
With 5 squares betwen them it would not be needed or the pawns would be allowed to make the double step move after moving only one step on first move, to make the game faster.
Said that I think the double step rule should be changed to something like that:
"If there are 6 or more squares between the square that you are and the promotion squares, you are able to make the 2 steps move"
Well, this rule will fix most problems. But you will have problems if you play one variant where there are promotion squares at different distances (6 or more squares between the closest promotion square, 6 or more squares between the furtherst promotion square?).You will also have problems with variants where the pawn can jump or do something else that will make him move more than one square naturally (so, 6 or more squares between him and the promotion square? 6 or more moves between him and the promotion square? 6 or more turns [if you can move more than one time in a turn] between him and the promotion square?
Anyway I think this "variant" needs more rules:
1-Castling is a move of the king or a move of the royal piece? (On my opinion its a royal piece move)
2-How check/mate works on a game with 2+ royal pieces? You need to mate only one piece to win? Mate both on same turn? Check/mates rules only take effect after there is only one royal piece on the team? Mate means enemy have no way to make all his royal pieces not be consecutively captured on next moves?
3-How promotion works? The piece that pawn (or another piece) promotes to is a new piece or a changed pawn? This would help to check if a royal pawn keep royalty and if the pawn moves go to the new piece (and so if the piece will be able to castle or not)
4-What happens when pawn start at a promoted square? Player promote before game start or on his first turn?