I got a reman alternator and a new voltage regulator today. I have them installed now.
Unfortunately, I still have the short, which gives me around 12.65-12.70 volts between the connector and the negative post on the only connected battery. I tried starting it, and it started and ran great. I had a meter in the cab with me and got between 11.8 and 12.4 volts, with the tach at 2200. Also, the factory gauge was bouncing up and down, coinciding with the voltage spikes (If that's what you'd call 12.4v)
It seems to me, as if the alternator is trying to charge, but something is holding it back.
I intend to pull both wires from the starter and trying my short circuit test again. That's the only thing, that I know to test next.