So sorry for not bothering with any of the responses before now, but thanks for all the suggestions!
Since the last post, I've gotten the bike running when the issue magically disappeared, but I never actually figured out a solution and it has since reverted to its non-running state. I have looked at the starter relays, and they are not welded open but sometimes they stick or the solenoids inside click around depending on the state of the battery charge. I find that the top 7.5A fuse draws the most power, unsurprisingly. I still need to dive in with a meter and see what the voltages are doing on each of those circuits. I have also removed the starter and cleaned the brushes/commutator, but I will need to order a set of brushes as the ones I've got are getting too short.
In order of the questions you've asked:
Welcome! Has your bike been converted to a cafe racer?
No, I was originally planning to do that (I know it's unoriginal but I wanted to machine the rear suspension from the Retrorides bike as a school project) but have since found a Honda CBX that will be taking all the funds not necessary to get this thing running and riding so I have a bike in the interim. Sorry K guys, but that inline 6 was too sweet to resist 😍
One other point, the accessory plug is usually connected directly to the battery. It may or may not be fused.
Check it's wiring very carefully, making sure that there are no bare spots in the wire that can touch the engine or the frame.
It's not uncommon to have the starter relay weld the contacts when you try to start with a low/weak battery. Is the starter trying to turn or get hot?
Also, if you're lucky, starting from the source, maybe you shorted a cell of the battery, reducing it to 10 Volts.
The fuses might not have blown, but may be cracked, which sometimes can't be seen.
I know the starter relay is being a bit finicky, but I'm not sure if that's due to something else in the chain. The battery is happy at 13.1v, but I should probably replace that top 7.5A fuse. When everything in the cluster dies, the whole bike just quits. No noise from the fuel pump, nothing from the starter. As of late whenever I try to start the bike, I've had it on a tender/charger. I turn the key, center the kill switch and hit the starter. One click from the Ebox, clock fades and lights die, and it won't do a thing before I turn off the ignition and let it sit for a few hours.
I appreciate all the help from you guys, and I've really got the kick in the pants to get this thing done now that I have a few weekends/nights with some time before the really nice fall weather rolls around in November here in ATL. Hopefully I'll have it running soon! If there's any other suggestions I'll try to be a bit more responsive this time.