I see you're counting Tournament of Champions as slams... I think you should count WFT titles in modern era then.
Anyway I think you should stick to wiki's count, perhaps subtracting amateur slams. As I said before, I think Rosewall leads the list with 19 (discounting 4 amateur slams)
I AGREE! This is getting beyond silly. Pro Slams: Wembly, French Pro and US Pro. Open Slams: USO, AO, Wimbledon, French. The way things are going here now, every other tournament will be a slam in order to promote one's favorite players. Rosewall has 19 or 23 sanctioned slams, ACCEPT THE REALITY! I am not saying he is the GOAT, there is no one GOAT, but he deserves to be in the top 5greatest of all-time. He also had 5 years as undisputed or joint #1. Joint #1, is still #1, IMO. Again, Tilden did not do that well in the mid-late 20's when the French top 3 were competing in the same slams he was competing in.