Many, including myself, have run into issues with steering wheel shakes right around 60 mph with both stock and after market tires/wheels and all sorts of tire sizes.

This may not work for you, but through trial and error I'll share what worked for me and hopefully this will help you.

There are three key things here to get the balance right.

1. Road force. Most know this, but make sure the shop checks it.
2. Adapter plate. Make sure the shop uses these instead of the cone adapters. This is important for Toyotas

Now for the most influential factor in my case:
3. On some Hunter machines, there's a program that's called "Smart Weight". If you're struggling with balance, ask the shop to turn it off. . For me, the above points 1 and 2 were perfect but the steering still shook. Everything, even the alignment was checked and yet I had shimmies and shakes.

Turning off "Smart Weight" and rebalancing resolved the issue immediately and seemingly consistently (twice now on different tires and thousands of miles apart). I'm not an expert on what that program does, but apparently it's counter-productive for balancing in some cases, at least.

My work was done as Discount Tire, so likely the DT around you will have the same Hunter machines.