One thing to keep in mind is your check of the alternator was a year ago, IIRC from your initial statement. And since that time you've been running on battery power, then you charge up the battery when it goes dead, yes?
So it's hard to know what is the actual problem, since the V. reg is un-testable except for testing the wires between it and the alternator. The battery could be bad at this point from cycling it from charged to near dead so many times.
I suspect that you will find the V.reg to be the issue, and for what it costs that's a good thing.
So I'd verify the wires, then get a V. reg, if the wires check out, and try it out. This way you'll likely solve the problem, BUT you may end up needing a new battery too. One step at a time, post back results.