See if the shop has a Hunter Road Force Touch GSP9700 tire balancer. The machine basically runs itself, so almost goof-proof. Plus it does a road force variation test to see how the tire reacts under a load. Only one of the few tire balance machines that can do this. Also checks for tire runout (bent wheels, tire pull issues), damaged tires (changes in density, high or low spots), and tire conicity (some tires can wear down into a cone instead of evenly as a cylinder)
This will eliminate a lot of the vibrations that people have seen. Sometimes, it is the technician skill that is paramount. I've seen tires that cannot be balanced, unless you spin then 180degrees. Generally not preferred, as the tire is marked where it is heaviest and lightest - but sometimes it helps with vibration/uneven tire wear.
Playing around with tire pressures can also help - some tires do between to more or less tire pressure. General rule of thumb - use the placard PSI (inside glovebox, on driver's door jam) to find out the OEM tire pressures, usually it is 30-32PSI. Look at the tires and note their max cold inflation - that usually runs from 44-51PSI. Those will give you the range of acceptable tire pressures. Personally - I start out within a couple PSI of max cold inflation and bleed the tires down until I find a speed spot. Don't worry - the tire won't "blow up" at the max cold inflation. In fact - some people run some incredibly high tire pressures as part of hypermiling. Just note that not all tires can run overpressure - as long as you stay at or under the cold tire inflation (tire manufacturers have already factored in a safety margin and temperature variations - ie, they know that pressures will be higher with a hot tire.
Ideally, you want to run a tire contact pyrometer and measure temperatures across the face of the tread after drive the car hard (high speed, hard corning, braking ,accelerating, etc). If the pressure is right, the temperature would be even across the face. Problem with that - hard to take accurate measurements of temperatures and the ideal pressure may not be the right pressure for your driving situations.