Hello and welcome Kane. Thank you for a complete and well written post! Holy Lord it's nice to have a little info to go onUsually we get the FaceBook dropouts that post "HELP!! my bike won't start!, tell me what it is right NOW, you idiots!"
These are pretty simple machines, you've done a great job of checking a lot of things, so let's try a couple quick checks and maybe we get lucky:
You have ECMspy. Whats the current AFV and EGO correction? I would be OK with re-setting them both to 100.
Repeated cold starts (even with a perfectly running Buell), will foul plugs quickly. You've probably just replaced them... but if you've tried to start it more than a couple times, do it again... every time. I know it's pain. The fact that it starts ok and then runs bad means they're probably OK, but it is free!
The O2 sensor isn't active that fast on a cold engine, so it's not doing anything. However running bad will clog it fast, you might want to get one to swap out AFTER she's running better. Check the parts interchange thread for applicable numbers, or I have one I can send you.
For the TPS re-set, I want to make sure you are performing the WHOLE process, (using the idle screw set to 0, first), re-set, set TPS degree... and not just punching the TPS re-set button? It will act exactly like you describe if not done correctly, and its possible the PO did that and screwed ya over (PUUNNN!) before you even bought it.
Backfiring through both the intake and exhaust is most certainly a timing issue. Good that its statically timed correctly but the fact that it runs ok for 20 seconds and then starts the issue tells me a CPS (or the circuit) could be failing. CPS like to fail with heat. There is a single wire from the CPS to the ECM (GN/W), gets modified for timing each cylinder then it splits to 2 (Y/E and BE/O) and goes to the coil. Check continuity while wiggling (the wires, lol), and use a timing light shining on the sensor to see if it's jumping around while running. Alternatively just replace the sensor. I hate throwing parts at something but you're pretty far down the wormhole right now.
This (Page B-19):
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from here: https://buellmods.com