You forgot BA, although they really don't have F. Granted they sell it, but it's more like a good Business Class.
I can understand your not wanting to fly AA although my recent LAX-LHR flight was surprisingly good.
But can't understand your reluctance to fly QR as my experience has been just the opposite, very positive.

FWIW, my overall ranking of the international F products I've flown.

1. Air France
2. Garuda Indonesia
3. Qatar
4. Emirates
5. Etihad
6. Lufthansa
7. Cathay Pacific
8. Singapore
9. Swiss
10. ANA
11. JAL
12. Qantas
13. Korean
14. Malaysia
15. Asiana
16. Thai
17. American
18. British
19. Air China
20. United