My first thought is that some belt in a tire is deteriorating or moved.
I do not think the tire shop spins the tire fast enough (65mph) to notice the shake when its on the balancer and if the tire is not taken off of the rim of course then you cannot see inside tire.
And sometimes thats where the deterioration will show up.
And there are these possibilities:
Warped brake rotors. The rotor hits the caliper every tire rotation causing a small bump in the steering wheel each time.
Shifted belt in tire or other defect in tire including irregular wear (tire rotation under these conditions will on move the vibration felt), loose lug nuts, worn inner tie rod end bushings, loose mounted or internal play in the rack and pinion steering gear.
CV joint could cause this.
Worn struts which had can cause a tire to wear unevenly (flattening one side of the tire). That causes shimmy at higher speeds.
These are not all my ideas but gives you some things to consider.