Regarding Fivequarters, Red and Green Pawns can move only within the long orthogonals a-d. Thus they can capture from b to a or c, and from c to b or d, but from a only to b and from d only to c. Likewise Yellow and Blue Pawns as regards long orthogonals e to h.
So what happens when Lemniscate Pawns go 'off-track'? From what you've said, if the Pawn starting on f1 captures from l4 to t2 it gets fast-tracked to promotion to Steward, but what if the one starting on b4 captures from l1 to g3? It ends back on its own player's part of the board! Does it flip over and start behaving as if it had started on f3?