Remove the loot restriction entirely, it's il80, it's dumb. The RNG is so bad, that I can't get a piece i want to drop as is, no need for loot lockout.

Better yet, make it so you can need gear and no lockout, but can only greed 1 piece a week. This would allow people 1 or 2 pieces a week (thanks rng) and prevent them from hoarding all the greeds for other jobs.