Another method would be paying off Chase, then paying off high interest to low interest.
Once your lower utilization reports, app for the Chase slate card and transfer your balances.
It's tough time for you. The moment you paid Amex, Citi, and Chase (maybe), they may reduce your credit.
AMEX: I would be suprise if Amex hasn't call you already or even give you FR. They will reduce your credit if you don't PIF soon.
Citi: Depends if you are still on 0% promo, be careful they will reduce your CL.
Chase: same as citi.
I would do as follow:
PIF on chase
What ever you have left distribute evenly on BOA, Discover, and Citi
Dont' have to follow my advice because I maybe wrong.