An update:
TL;DR: I ended up getting the battery to charge after disassembly. EDIT: However the charging circuitry seems to be the fault that originally lead to the battery discharging.
I left the phone sitting in a drawer until today, as I didn't have time and wasn't looking forward to disassembly. I felt like I was in the mood today and that I had nothing to lose, even if I broke something along the way.
I followed this guide by the way (read all of the tips, as the author is very correct): https://github.com/imax9000/fxtec-pro1-teardown
I managed to not do too much cosme