My thoughts...

1) Keep the 30 min timer on Ifrit, Moogle and Garuda fights and any fights like it. Still have achievements for speed runs and stuff like that. Make the fight accessible in the same manner as i is now, 15 min cooldown for win and 5 min for loss. Raise drop rates based on wins as mentioned earlier in this thread.

2) Make dungeons longer by adding more content to them like NPC rescues, more bosses (maybe some mini bosses with lower drop rates on the same gear while the bigger end bosses have better drop rates), some puzzles or mini-games inside the dungeon that have different solutions to them each time. Extend the cooldown timer to one week -1 hour (for late comers). The biggest thing is to get those damn timers out of dungeons. Nothing ruins an (don't shoot me for using this word) immersive experience than being on the clock. Let people enjoy what they are doing. Let them think about what they are doing. Give them more things to do in an instance and they will explore it more thoroughly. Gear the achievements for dungeons toward completing objectives in the dungeon rather than clocking them with a stop watch so they miss the whole damn thing. An instance like a dungeon, a ruin or a beastman hold should be a 2-3 hour experience not a quickie in a bar bathroom.