Backfire-after turning key off

Nope. The ballast is bypassed when cranking, so if ballast is bad it will try to start, but die in run.

My guess is a short on the coil -, or bad transistor in ECM. When you turn it off, you get a spark, but it is not in time with engine.

The other possibility is pickup related, faulty, gap too wide, or connector issue.

Not if the fault is no power on the start side. :D
The ignition switch can be bad on the start side and fire a spark only when you let go of the key, but most engines I have had fire up at that point anyway just because they are already spinning.
They don't usually backfire though as I would call a backfire.