I had the same problem with a 2008 GT that I owned briefly. After a week of owning it I noticed the hum/drone/resonation noise and took the car to the ford dealership. It sat at the service department for a total of 28 days. They kept it for two weeks and replaced the transmission twice, the driveshaft, new tires, new wheels. After the two weeks they gave it back to me and said it was fine. It still had the problem so I took it back and they kept it for another week. When they gave it back the second time they "fixed" it by taking the transmission, driveshaft, and axle off another car and putting it on mine. When I picked it up and told me this I wasn't happy about it, and the car still made the noise. I took it back for the third time and the flew in an engineer from ford for a week who put sound deadener all over the car, replaced the ring and pinion, and rebalanced the driveshaft. When I got the car back the third time it still made the noise. I was able to get the car bought back by Ford under the lemon law. It was replaced by a 2010 GT and I haven't had a single problem with it. (knock on wood)
If you ask me the problem lies in the body or frame. Some frames must just transmit more resonance. On my '08 they basically replaced everything after the engine multiple times and nothing worked on that car. The only thing they did not replace was the frame.