Got back to checking out my BAP issues.
Removed it, took off the end plates to see what it looks like inside, and was disappointed to find just hard black goo and nothing else.
Apparently Kenne Bell covered up all the guts in that stuff, and all you see is a few wires coming out of it:
I found 2 iffy connections, one for the 17V wire going to the wire at the fuel pump driver module, and one at the main power wire going into the BAP.
Took them apart, re-did the connections with fresh wire and solder, heat-shrink tubing and electrical tape where needed, and also cut back, stripped and re-connected the wires for the un-used Hobbs switch and adjusting knob, since this setup is wired so the BAP is always putting out 17V.
Put it back together and tested it, and got a solid 17.09V out of it.
So there's a chance that all my fuel issues were caused by bad connections.
I'm not 100% sure of it, but at least one of the connections was pretty crappy, and it's now 100% solid.
While I was at it, I re-located the grounds for the relay and the BAP, and added a quick connect/disconnect setup for the 17V wire going to the FPDM from the BAP, so if I have to remove it in the future, I can easily unplug things and pull it.
In the above pic, the blue wire on the right/bottom is the upgraded power wire coming direct from the battery (with a 30A inline fuse near the battery), the thick red wire provides power to the BAP, and the black wire with the yellow connector close to the FPDM is the one providing 17.1V to the FPDM