Think I've worked out that it's the control board - specifically the defrost timer. This sucks, because the replacement board is at least $280 AUD to source. But I've enough skill and tools that with some research and testing, I might be able to repair it.
I was setting up to test the defrost element (to see if it was actually doing anything), b/c it's entered the 'running indefinitely to reach a temp it can't reach due to frost buildup', and when I plugged it back in, it did not start immediately.
Contrary to prior behaviour, this suggests that the thermostat is working, and that it's doing something. But it's not proven yet.
I also know that the defrost is run for ~5 seconds on first power on for the fridge, so I'm going to be testing this by cycling the power of the fridge (also to help not overwork the compressor)
And if I can get it to defrost a bit without needing to do it manually, it'll be way easier on my patience and energy.
I'll be getting a spare fridge a friend has around soon to swap to, but it'll be temporary - I intend to repair this one - it works extremely well, not a single case of coolant leaking or anything.
And it might just be a dead capacitor or relay, and those are so easy to replace.
Saving hundreds of dollars AND guaranteeing the good operation of the fridge would be a HUGE win, so.
And I'd like a huge win.