Very good! Blocking with bd2 actually allows you to extend this to a mate in 12 but as you mentioned it’s easy to see after Qxa1. Stockfish gives the initial position #9 which follows pretty much exactly as you stated. The only reason it’s 9 is because white can extend by either sacrificing the queen on g7 or giving a pawn check on h7. After the f file is open white is simply throwing all their pieces in the way to extend the mate.