Well, I'm happy to say this problem is resolved, and let me tell you, it was a journey. Let's start from the beginning.
About a year and a half ago, we got a wind turbine that we hooked up to our system. About the same time, my dad reworked the wiring in the power shed before insulating the walls and putting wall and ceiling panels in. Keep that aside for the moment. At the same time, about a year ago, we got a set of batteries we could hook up as a secondary power source (we have two DIY inverters hooked up to that collection, as well as a singular Classic that is using power from 4 combined arrays, from a combiner box that is right there in the shed (3 of the 4 arrays were already wired into there on an Outback controller before I added one more array and hooked them all up). Before I got the batteries hooked up properly (custom copper bars connecting the necessary series and parallels), that charge controller was also hooked up to our main battery bank. My dad had associated the start of the problems with the installation of the wind system. That turned out to be a red herring that took me a while to work past.
Now, two separate things happened that probably wouldn't be critical if they had happened separately. First, there was apparently some confusion as to what wires were the negative wires for two of the four arrays going to the secondary bank. So, when my dad did the rewiring, he took those two negative wires and connected them to ground, thinking they were grounds. Like I said, not super bad, those two arrays just wouldn't work. Or so you would think. Because of that rewiring my dad did, there were still a couple wires over by the combiner box that I could reasonably assume were the negative wires for those two arrays. So, OK, I hooked them up. One was a dead wire, made no connections. However, the last one wasn't a dead wire, wasn't a negative. It was ground. It was connected to ground right next to the charge controller that was having the most troubles with ground faults. Again, it wasn't an issue, necessarily, because that array just wouldn't work. And so, the kicker is that those two arrays were actually still providing power to the secondary battery charger. Through ground. Through the connection right above that charge controller. Which would explain why it was so intermittent, because it would require some kind of special circumstance in the combiner box array to trigger something in the main array.
So now I've hooked everything back up (I had to switch the controllers between the main one on the main bank and the one on the secondary bank to try to diagnose faulty hardware, since that former main controller was 5.5 years old). Ethernet, FollowMe, all arrays, all controllers, even the wind system. Only finished it up this morning, but so far everything's back to peak operation, no ground faults. As my dad said when I told him, it looks like we found the smoking gun, and I agree with him, so I'm confident the problem is actually resolved, and after a couple of days with the front plates still off, I'll put everything back to normal and finally be able to completely clean up in there.