I can search up to ply 12 by asking the program to limit the search to pawn promotion moves only. Unfortunately, only the known 6. gxf8=N# determines all the previous moves in this search. But a few moves do determine at least the final position.
5... exd1=N# (7 solutions)
6. gxf8=N# (1 solution)
6. d8=N# (2 solutions)
6. fxe8=N# (8 solutions)
6. gxh8=B# (16 solutions)
6. fxg8=N# (37 solutions)
6... c1=N# (6 solutions)
6... fxe1=B# (6 solutions)
6... h1=B# (6 solutions)
6... dxc1=B# (8 solutions)
6... bxa1=B# (16 solutions)
6... cxb1=N# (210 solutions)
.+: discovered check only
++: double check
.#: discovered checkmate only
##: double checkmate
e.p.: en passant capture
5. dxe8=B.+ (4 solutions)
5. dxe8=N.+ (4 solutions)
5. dxe8=Q++ (4 solutions)
5. dxe8=R++ (4 solutions)
6... fxe1=N## (50 solutions)
6... fxg1=N## (84 solutions)
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