There’s one quick check that could be worth doing before getting to the de-soldering stage. Try running the machine with the socketed PIAs (UC6 and UC7) removed. Faulty PIAs are not uncommon and can cause display corruption. You don’t need to reconnect the keyboard to do this. An otherwise working PET will happily boot to BASIC without the PIAs although there won’t be a cursor and some of the interfaces won’t work.
Alan