He may be a great mechanic but a not-so-great tire person. Understandable. You need a shop that specializes in tires.
I buy my tires from a local shop that does tire installation and balance. They don’t do wheel alignment, however, so I have to go elsewhere for that, but they’re really good at what they do, so I keep going there.
Seems odd that TireRack would send you to someone who “does not do tires.”
Your problem is not insurmountable, you just need to find the right shop to balance/align your car so it drives the way it should.