Remove the stabilizer and take it back to the front end shop. It sounds like tire balance if it just start vibrating on it's own. If it starts when you hit a bump, it's most likely front end alignment.
Check the bushings on the shock absorbers. They are not the problem, but if you find one worn much worse than the others, you have found which wheel is causing the problem.
I had a similar problem with my '55 T-bird, it just started shaking at 60 mph. I took it to a mechanic who was recommended by several people I worked with. They had all taken there cars to him and swore that he was great. Well, I take the T-bird up to him and the first thing he does is a front end alignment. When I get it back, I take it out on the interstate and no change.
The next day, I take it back and he does a wheel balance. When I pick up the car, he tells me that he did a static balance and then put them on the car and did a spin balance. He tells me that he had to add a half-ounce to the left front. Back out on the interstate and no change.
The next day is Saturday, so I decide to look into it myself. I notice that the left front shock absorber is loose and the rubber bushing is part worn away. I took the left front wheel off and found the problem right away. There were two pieces broken out of the lip on the brake drum. It looked like the previous owner had set a jack stand under the drum. There is no way that a static balance followed by a spin balance on the car would not have shown a problem.
Do a visual check yourself. Take the wheels off. Look at the rotors/drums. Check the tires for a small bulge indicating a possible slipped belt. I do 80 in my CJ all the time and I don't have a problem.
I've replaced so many parts that my old Jeep has become my new Jeep.