FARM ANIMAS! Seriously, if all 6 people take the time to farm 3 animas each (one of each kind), the things aren't nearly as bad as they are made out to be. Your MNK can easily solo the mobs on the first floor, or even do the Fellowship NPC investigation quest and take him/her with you, set to healer. The recollections dropped by the mobs vary depending on which crag you're in:
Recollection of Pain --> Hysteroanima
Recollection of Guilt --> Terroanima
Recollection of Fear --> Psychoanima
In Promyvion-Dem:
Wanderers drop Recollection of Pain
Weepers drop Recollection of Guilt
Seethers drop Recollection of Fear
In Promyvion-Holla:
Wanderers drop Recollection of Fear
Weepers drop Recollection of Pain
Seethers drop Recollection of Guilt
In Promyvion-Mea:
Wanderers drop Recollection of Guilt
Weepers drop Recollection of Fear
Seethers drop Recollection of Pain
Hysteroanima: Stops empty from using special attacks
Psychoanima: Stops empty from using physical attacks
Terroanima: Makes the mob run around the arena, but is unable to be attacked by melee.
Don't skimp on meds either. A handful of hi-potions for melee, and ethers for mages, can make a world of difference. And don't forget re-raise earrings for the trek up. It sucks getting to the third or fourth floor and wiping. At a minimum, the WHM should have RR up at all times in order to get the rest of the party up.