Since posting my original request, we (by "we" I mean a man completely unrelated to the parties involved who had unrestricted access to the ATV w/ the freedom to troubleshoot properly) discovered the problem with the ATV. One of the two starter relays in back was faulty. Which one, I couldn't say as a long drive to a repair shop some hours away was preferable to properly testing the relays & now I don't care.
There are two relays/selenoids/made-up-term-to-sound-smarter in the rear (one is for the starter motor itself, one is for (?) the entire circuit (if I remember correctly). On the ATV in question, both are snugged up under the seat/rear fender and accessed from the back (no cowls, etc. need to be removed). In any case, those were tested a number of times via the manual provided and tested within spec. However, they were only ever tested after the motor was successfully started because a certain someone insisted on doing it that way no matter what I said.
Unless you have a tester with alligator clips and long leads, you'll need a helper to test. Since you're a man, you'll find it easier to get your helper to do something you ask without arguing or lying about what he is doing with the switches while you're on the cold ground getting dirty trying to figure out what is wrong with it. The point being, even if they test good, they may still be faulty depending on WHEN you test. They run around $30-40 and if you don't want to try replacing them outright, test while it is acting up.
The only other issue that may have made sense was a problem with holding charge. That was a serious contender with a certain relation & the reason it was sent to the shop. Initially, it wasn't a bad idea, until the vehicle "fixed" itself for some weeks, but around here we don't let facts get in the way of a long, arduous drive.