Engine stays running without key in ignition (and more!)

Okay, I checked the voltage at the battery, alternator, and VR while idling.

Battery ~16.4
Alternator ~16.4
VR ~14.6

I also checked the ammeter, and I got -0.75 when the needle was pegged to the right. I'll be honest, I still don't quite have a firm grasp on what I'm dealing with, but as you said
Voltage of the J2 circuit should be fairly close to the votlage measured at the alternator output and the battery at hte same time.
If there is a big difference, then that indicates resistance to current flow.

so, I thought I'd swap voltage regulators to see if there would be any change, and BOOM. Problem solved. No more erratic ammeter needle. I still wonder if there could be a problem elsewhere that hasn't made itself obvious yet, so I'm going to keep checking.