I think that the best and most fair solution would be to have dungeons, trials, raids, etc. have an individual minimum DPS objective. If you fail to meet that objective you are not able to roll for loot or it doesn't count for quest completition.

Or add time objectives to dungeons, example finish within 20 minutes and you get bonus gil/exp/items, finish within 21-30 minutes and you get normal exp/gil/items, take more than 30 minutes and you don't get rewards.