I know this sounds simplistic, but make sure your tire pressures are spot on. I had the same shake (between 73- 79 mph) and thought I would have to live with it.
The previous owner had spent a lot of money chasing the same shake, to no avail. I replaced the front tires and had a dynamic balance done and it helped a little but it would still show up now and then.
Back in March I brought the car out of storage and double cheked all systems and made sure the pressures were correct, and set out to take a short trip.
Watta ya know !! No more shake (except a little flat spot vibration). It's now shake free up to 110 mph.
Also make sure a belt hasn't twisted in one of your tires.
Good Luck !
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