Is it permissible to tie each corner with a different method?
There is no prohibition that I know of for tying a different method on each corner – I have tied talitot like this in the past. Each method fulfills the d’oraita requirement of a “kesher elyon” (top knot) and one “hulya” (three winds) and all attempt to fulfill the various Rabbinic requirements stated in the Gemara. That being said, it is my personal opinion is that one should be consistent and tie all corners according to the same method. If one wanted to fulfill various methods it would be preferable to have different talitot with different methods. But again, that’s just my opinion.