So here's the breakdown:
1. Queue specifically for FoS (or whatever)
2. Clear trash to the boss and hope for a hilt.
3. Engage and fight the boss.
4. Get the boss down to a point where you feel comfortable that the group will finish it off without you, but not so low that they'll kill it before you get a chance to re-queue. Take load times into account here. 25% usually works out fine.
5. Drop group
6. After you load back into wherever you were, immediately re-queue for FoS (or whatever). You will not have the ditcher's debuff. You re-queue because sometimes you'll get saved if you don't, it's buggy.
7. Within about 30 secs you'll either get a system message that says your saved and got a badge/keeper shards OR you'll suddenly have mail that contains the badge/keepers shards.
8. You are not actually saved, and are in the queue to go again.
9. Repeat