Strangely I was about to suggest the driveshaft when I read the OP. I would not like to buy a new one, but I would try to find a way to isolate the issue and see if it could be the problem. If other people are not familiar with the drive shaft on this year, it is not a solid normal/typical driveshaft. (I am uncertain about later versions of the mustang) It was designed with a floating internal weight system which is supposed to help with vibrations/oscillations. I have not read anything about what happens when this design ages/fails. It is also a two piece design with added issues of the additional connection and dampeners. So while I would normally never think about a driveshaft causing noise, it was something that came to mind after eliminating the more typical areas.
I would think examining the car on a dyno may help, not that I would get near it in that situation.
I would think examining the car on a dyno may help, not that I would get near it in that situation.