First questions first...BBA AFAIK is RANDOM with $99 specials. I did well by BBA. I just have changed my opinion about rebuilds vs. new. I was in the re-build camp as there is no re-coding, as long as you use a good vendor, and many have had good luck, but as many have had waste of time and money chasing re-build road. I have come around to new or forget it. I would get a new module regardless just due to age and if errors remain, then look at sensors using the test procedure rather than what scanner says. A new module will give you a peace of mind you can't get otherwise. So, I would do new module and if that did not take care of WSS errors, yaw sensor error, or whatever then just deal with those issues next.
Modules go bad due to heat. Their placement is terrible! That may explain why you start cold with no errors until heat from manifold gets to module. This is even more reason to suspect module itself. Get new module coded with an autologic if possible.
Look, for $99 you might as well try the BBA route, but I would not view the module afterward as repaired, never should be an issue again, done, forget it, etc. It would always still be somewhat suspect. They do not replace parts. They focus on solder connections. Biggest wires first. After repairing a wire or two, another even smaller wire can go bad. Good luck.