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

If you see that, shut it down and find the problem.
Apologies, but I thought that's what you meant with your original test. I thought I was to connect the voltmeter to the ammeter while the car was running (and showing the problem) to see what voltage the ammeter was seeing. I'll try again today, and also try turning on some accessories. Actually, all I have to turn on are the lights...no fan, radio, etc. Haha.

I'm guessing by hte time you changed regulators the battery finally came up to full charge since you put it on the charger.
I waited until the battery was fully charged before beginning any diagnostics. In fact, when my charger indicated the battery was fully charged/maintaining, I checked the battery with the voltmeter and it showed 16.6 volts. Could the charger have overcharged the battery? It's not exactly a high quality unit, just something I picked up from WallyWorld a few years back.

I REALLY appreciate your patience and great explanations along with the diagrams. I know this stuff is pretty basic knowledge to most people, so for you to take the time and break it down and explain it several different ways really says a lot. Thank you.