>The one with 3 sets has a single wire and a 2-into-1 pigtail.

Okay, that makes sense.

I guess the next thing I'd try to trace out the circuit with a continuity tester. Start with the single wire outlet (end of chain) and figure out where it goes. Just short white/black on that outlet, and test continuity at the other outlets. I'd hope to narrow down where the GFCI load is supposed to connect through this exercise, as well as verifying all the other wiring.

Not that this fixes your problem, but it narrows down the problem circuit. It could be a drywall screw through the neutral, mice, or some other break.