I cant answer your question because I dont know =/
I remember how to do it quickly.... I think.
1. Your in fort hope, im in the dungeon I send you a TP
2. You kill everything in the dungeon without looting the quest items, most or all mobs will drop the quest items.
3. you then go around collecting the quest items after all monster in dungeon are dead.
4. When You open a TP, it will take you to Fort Hope from discordia dungeon.
5. Hand in quest, and take the quest again.....go back in your TP, and start looting the rest of the quest items that will be on the floor due to killing everything.
6. When there is no more quest items on the floor simply walk out the dungeon without using the anchor stone reset and repeat from 2.
If you dont use the anchor stone to come out, you will never bind your self to discordia, meaning your TP will always take you back to Fort Hope from inside the dungeon. All the monsters in the dungeon will be dead and every floor will have quest items on the ground so all you need to do in theory is hop in and out of the TP to collect quest items.
If you are receiving the quest then running to crumbling then into discordia > collecting quest item > running back through crumbling back into fort hope to hand in the quest then yes its going to take a hell of a long time.
Next time you are on just send me a /w and ill TP you into the dungeon you need. to try the method above.