It seems to have been missed so far that f3 is also a possible reducing move, it gains a king move, however, but loses both a knight and a pawn move. Therefore, we have a lot more choice and, in fact it appears as though, a full 20 moves are possible:
[FEN ""] 1. a3 a6 2. f3 a5 3. h3 b6 4. b4 a4 5. b5 e6 6. g3 Bb4 7. g4 g5 8. Bg2 Bc3 9. Bf1 Qf6 10. f4 Qxf4 11. Rh2 Qxh2 12. h4 Qxg1 13. h5 Ke7 14. h6 Kf6 15. e3 Bxd2+ 16. Kxd2 Qf2+ 17. Kd3 Qxe3+ 18. Kc4 d5+ 19. Kb4 c5+ 20. bxc6 Qc5#