What if the engine failure is from fuel contamination?
Then you won't get your APU started and generator failure on the good donk won't matter anyway.
Will a fuel imbalance become that big a deal that quickly?
You bet it will.
Fly the plane, deal with the engine failure,.......
I believe the PF is doing that from the start. PNF is carrying out the A/T,APU & crossfeed configuration.