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Do I understand correctly that the edge pawns cannot promote without capturing? Is that a feature or a bug?
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You understand correctly. Whether it's a feature or a bug is a matter of opinion I suppose. Pawns potentially getting stuck with only capturing moves is a natural consequence of a hexagonal board with players at opposite edges. Playtesting is probably the best way to determine whether that's an interesting new strategic consideration or just a nuisance.
If it is just a nuisance, then in place of castling, Delta-Nabla's own cludgy rule should probably be to give pawns the option of moving (without capturing) in the obliquely forward rook directions whenever they're not in a position to promote by moving directly forward, or perhaps only when the directly forward option is impossible due to reaching the board edge.