Not an A&P. Am familiar with how electricity works. Two points. 1 - The above doesn't sound like it has anything at all to do with an alternator belt problem to me. 2 - That the voltage regulator was replaced doesn't have any correlation with it working.
To me, troubleshooting non-intermittent electrical problems are generally way easier than mechanical problems. In this case, maybe put a significant load on the alternator while the engine is running and find where the voltage drop(s) is/are happening. And maybe even before that, determine what the base load on the alternator is, including battery, and make sure you don't have anything drawing power that isn't right, including the battery itself. Could be a lot of different things, the AP might be drawing way too much power for instance. My bet would be bad connections or wires from either hot or ground side of alternator, bad alternator, or bad or mis-adjusted voltage regulator. I suppose that's really just a list of the things from A to B, but way smarter to do a couple of tests than just start randomly replacing parts like some guy at the auto parts store. And to the other person's post, yep 13.3 is too low for the battery to be charging correctly.
Not meant to be mean, just a little tired tonight, trying to be helpful.