2001 Dodge Truck Front end of truck wobbles

First, mileage is in kms, so approx 83,000 miles.
I've just bought this truck from a dealer, very clean condition throughout and underneath.
When ONLY turning right, ONLY at highway speeds, 60-70 mph, the front of the truck feels like it is moving side to side. There is NO feedback through the steering wheel (shakes, shimmy, etc). It feels as if I am oversteering, then correcting, then oversteering, then correcting, etc. There is absolutely NO feedback through the steering wheel or the truck, other than the side to side motion. I have installed a brand new set of Dayton Tracker 2 tires and they have all been double checked for installation, balance, separation, etc and are all confirmed good. The front end alignment and components have all been checked and seem to be good. The alignment shop has a laser aligner and are very confident they have checked everything, but the reality is that the wobble is still there. In any and all other conditions the truck drives and handles as new. I look forward to your suggestions.