At the end of my rope here, had classic wheel shake at highway speeds and replaced rotors last April. By around September same symptoms back again went back to the shop and he replaced them under warranty and didn't charge me a penny so I'll give him that. Few months later same classic symptoms of warped rotors again wheel shaking like a leaf above 60 mph not much else that you typically would think it could be. Go back again and tell him to take it for a ride because believe it or not they must be warped again. Leave the car with him he says caliper was sticking on drivers side heating the rotor like an oven thus prematurely warping it so we replace both sides-rotors calipers and pads. That was about a month ago and it's already starting to shake again at highway speed. That's the 3rd set of rotors in 10 months, never had this happen before.
Given the age of the vehicle, your problem is likely with either the condition of the brake fluid, air in the lines brake lines, master cylinder, or slave cylinder. Also, the brake pad return springs may be missing or incorrectly installed causing the pad to drag thus heating up the rotor. Hopefully it is that simple.
If it hasn't been done a complete brake fluid change is more than likely required, and bleeding the brake system according to the manufacturer service manual (especially if equipped with ABS) will eliminate two of the possibilities for a relatively low cost.
You said that this is the 3rd set of rotors you've replaced. In my experience if the rotors were heated up to the point of deformation, the caliper was in need of a rebuild to replace brittle and broken dust seals to keep debris from causing piston to hang up after the pedal is released as well as other functions.
If all the above is done correctly all that remains is the master cylinder. Of course there's a remote chance the ABS unit, brake lines, proportioning valve, could be the cause but rather unlikely.
If the vibration symptom is not related to the problem of the brakes dragging the next step would be tire related issues like condition and balancing then hub and wheel runout.
Good luck and I hope that helps.