You don't mention checking the dropouts (fork ends) for being parallel after your cold set.
I once had a used bike that had funky handling. I took it to a competent shop with dropout alignment cup-tools and they straightened the dropouts to parallel.
The handling was transformed! A much better ride was the result.
I'm not knocking anyone's skills here. But anyone who can tie a pair of shoes could follow that string alignment procedure.
It takes top skills to produce a nicely riding bicycle. From now on, I take all my used bike purchases to a professional frame maker for alignment.