My 2003 Ford Excursion had this same exact steering "wandering" problem. We took it to the dealership a few times, while it was still under warranty, to resolve it, but they were unable. Different tires, different pressures by me never resolved it either, so we just lived with it. Well, I lived with it, my wife didn't. She never liked driving it because of this issue.
I know that this issue was a systemic problem found in many Ford trucks in the early 2000s. Not sure when they resolved it, but they did. It was the only real issue I had with that Excursion. I never had a problem with 6.0L PSD.