It sounds like this car may or may not be a true GT. I have owned a True 66 GT Coupe. The car was complete when I got it but in sad shape. It was an easy sight to see it was in fact a ture GT.
I know these cars can and have been changed in many ways during the years, I have seen plenty of it. What you mentioned about this car is not good, like the front drum brakes and steering box. However, the good would be the metal support for the exhaust and the correct master cylinder. The door tag shouldn't matter because it will not tell you about what options were on the car, but if you could find the build sheet, that will be the Holy Grail. I found my build sheet wrapped around the main wire harness behind the dash. It was a huge surprise, just like Christmas. My car was made in NJ and they sometimes put them there or under the seat.
My 66 Fastback is not a GT and it came with a lot missing. It didn't matter to me as I know what's missing can be bought. I'm getting ready to paint it soon and that's when I will really see the light and etc. I was not in a hurry and it's been 2.5 years now since I had the car. All that is really left for me to buy is the Red Line tires and Style Steel Wheels along with a few small odds and ends that may cost $200. Not counting my paint supplies which I have not bought yet. I'm still deciding on which paint system to go with.
During the 2.5 years I rebuilt the motor, rear end, welded in new quarters, transsion/trunk pan, floors, full frame rails, have re-done all the interior, (going with the Mustang Sport Seat look), installed a rack and pinon, disk brakes and the T-5 is ready to install with the motor after I paint it first. Plus much much more.
Here's a link to how the car looked the day I picked it up. I paid $2,500 for it. KODAK Gallery | Photo Merchandise
I do think that $11k for the car your thinking about is very steep, not knowing for sure if it's a true GT or not. I would say $5-$6k would be more like it.