[f5fstop]

Could be:
Marginal lateral runout. If the spec is close to max, a vibration could be felt at speeds.

Bad wheel bearing hub will cause a vibration at higher speeds. (Had this on a vehicle once, at about the same speeds you state.)

Force variation of the tire/wheel assembly. Only way I know to verify this is to have the tire balanced on a load force balancer.

Excessive runout of the prop shaft or pinion flange.

If the tires were rotated and the symtoms remained in the steering wheel, it most likely is not force variation, but....

Does it shake worse if you apply the brakes over 45?