I'm always hesitant to do the follow up post, but I read so many of them that rejoice in their success of fixing the issue, then a day or two later come back to report that the problem persists.
I'm cautiously optimistic that the battery was the problem. I bought a new battery on Monday. It has been in the 30s every night since, and the truck has fired right up every morning. Still don't know why AZ's load tester said the old battery checked out fine (it still has 12.4 v sitting on my garage floor), but I'm fairly convinced the guy didn't know how to either use or read the tester.
Once again, thanks to everyone that helped with this!