Um... FATES are the fastest way to gain GC seals in the game
Nope. The only ones that will achieve a decent rate are high level "uncapped" FATEs, which you won't get to do for most of your atmas.

You will get seals much faster by spamming Brayflox and picking up all the i70 gear that people inevitably skip while speeding through the dungeon. It doesn't even have to be Brayflox specifically, any level 50 dungeon will drop i55/60/70 gear that a lot of people won't even bother to lot.