1973 Dodge Dart sport speed related shimmy

Tie rods and ball joints have all been replaced. Tires and wheels have all been professionally balanced and this started before I bought and installed the new front and rear tires and cragar SS's. Shackle, leaf mounts and u-bolts have all been checked out. I take my car to well known reputable local shop shop since I can no longer work on it myself and have faith in them that they aren't misleading me as they don't ask for payment if what they do doesn't fix the problem.