That's a good 2 gen version of that parity alg, but I prefer this one just because it's a little faster (for me):
Edit: To solve the "triple parity" as you call it, solve two of the edges (I use E layer) so with the edges parallel vertically, I do (just the middle inner slice) E' R U R' F R' F' R E , then just do the OLL parity alg (r U2 (r) r U2 r U2 r' U2 l U2 r' U2 r U2 r' U2 r' ) for the last edge.