Load your team with Gadgeteers, and equip your party with the accessory that nulls sleep and doom. Then use the Gadgeteers doom spell till it chooses the right side (most likely the first or second try), and follow it with the sleep spell till it chooses the right side. Now wait three turns and voila - you've won. I have a five moogle and marche team specifically for this. Multiple Gadgeteers + proper team equipment is always a dangerous combo.