Qxh6 stops dxe3 due to a mate threat. But Bxg6 might be stronger due to the threat of Bxf7 (or Qxh6) So, Bxg6 (Rxh6 seems to lead to the same place) fxg6 Rxg6 Qxg6 Kf8 Qxh6. Then how we get another piece to the party? Back to f5 but that seems slow.

f5 Qd5 Qxh6 with a possible mate on h7. Or f5 Bd6 Rh3 (or maybe we can ignore the threat of Bxg3 and push on with fxg6, white will have to give up the c6 rook)