Have you tried the inner tie rod? My 2000 gt had that problem when hit the brakes the car shook like crazy. I jack up the front and tried to move the wheels side to side and had play on the drivers side and warped the rotors in the process. I had the inner replaced $27 bucks at advanced auto parts and did the rotors and pads at the same time and it fixed the problem. Might as well do the outer since it would already be apart. Instead of going to a shop and getting raped for a few hundred or more in needless parts and labor that would seem to be a good place to start. Good luck.
