Another attempt based on OP comments: "From your new 7-move solution, the first full four moves are entirely correct. Reconsider White's 5th move-that is your first one of your edit."
1. Qa4 Rxf3 2. Qa6+ Qxa6 3. bxa6+ Ka8 4. Ba3 Rxb1+ 5. Bc1 Rb8 6. Bb2 Rbf8 7. 0-0-0 ..
From the title To Win The Right To **************** I think the asterisks refer to queenside castling which means the title was actually To Win The Right To Castle, which gave white safety from being threatened to be mated and the advantage in the following moves.
From OP clarification: "I mean to say that by White to win I meant for White to reach a winning position. I also forgot to mention that the solution is 7 moves long The title is a bit of hint as to what the solution has."
Possibly the solution was as Sconibulus answer suggests with elaboration assuming black plays suboptimal moves:
1. Qa4 Rh5 2. Qa6+ Qxa6 3. bxa6+ Kxa6 4. Kf2 Rh1 5. Nc3 Rh8 6. Bb2 Rxa1 7. Bxa1 Rxh7 .. then white would have advantages.
From OP comment: "White has....ways to avoid a stalemate, and capturing White's rook would not benefit Black at all. " add variant:
1. Qa4 Rxf3 2. Qa6+ Qxa6 3. bxa6+ Ka8 4. Ba3 Rxb1+ 5. Rxb1 Rf1+ 6. Kxf1 then stalemate since black can't move
Considering black always play the best move:
White won't be able to win.
Most of the white move would be a big disadvantage since no way out of mate from black without sacrificing a lot.
a) 1. Qb3 Qd6 2. Qg8 Qh2 hardly any chance for white to win left.
b) 1. Qb3 Qd6 2. exf5 Qg3+ either mate or draw from repetition moves.
c) 1. Ba3 Qb6 no way out of this mate.
Other variant doesn't seem to do anything better to solve the stalemate.
But if black was able to play suboptimal moves:
White would be able to win.
One of possible variant:
1. Qb3 Qe5 2. Qxd3 Qxa1 3. exf5 Re8+ 4. Kf2 Qe5 5. Qd7+ Ka8 6. Qc6+ Kb8 7. Qxe8+ Qxe8 8. Bb2 Kc7 9. h8Q Qxb5 10. Be5+ Kd7 11. Qg7+ Ke8 12. Qg8+ Kd7 13. Qf7+ Kd8 14. Qc7+ Ke8 15. Qc8+ Ke7 16. f6+ Kf7 17. Qc7+ Ke6 18. Qe7+ Kf5 19. f7 Qb6+ 20. d4 Kg6 21. f8N+ Kh5 22. Qf7+ Kh4 23. Qf4+ Kh5 24. Qg4+ Kh6 25. Bf4#
Apronus PGN Viewer
Disclaimer: I used Droidfish to spar my move against, and tweak the move for black suboptimal moves and play normally for the rest.