So far about two weeks and no new smells from the p-trap since cleaning with bleach water, rinsing then vinegar/ water.
Only time will tell if it was long term bacteria / mold in the overflow area that I killed off or if after 6-12 months the ptrap starts stinking again. I will say that when I sniffed the overflow hole for the reservoir I never smelled that bad smell, but when I undid the p-trap it was DEFINITELY that smell.
Everything is as clean as possible for now all the way to the pipe in the wall. It could have been caused by enough gunk in the ptrap but there wasn't much. It's almost as if each use of the sink let in enough gas from the p-trap that it made it's way up the tailpiece. Still not 100% sure.