Well figured I'd update this. I had to drive to Indiana (540 miles) after I left the dealer so I'm finally getting around to it.
They used the forced variance balancer today. All the tires were between 17 and 26 lbs of force. They also checked for out of round (all passed) and rotated them as well.
The result? Definitely better but not totally gone. It feels more chassis oriented now than steering which would indicate the problem moved to the rear when they rotated the tires. I guess I'll need to get another opinion on the out of round or just do it myself when I get home.
Perhaps I'll pull a tire off the 07' and put it on the rear where I think the bad tire is to see if it makes a difference. Can't hurt.
Making progress if only by the process of elimination. But still progress.
Now I also wanted to give a big thanks to Apple Ford of Lynchburg for standing behind their work. I only took it to them after I gave up on the shop that installed the tires originally. I paid them to balance everything the first time and they refused to charge me twice since then due to the ongoing problem. Considering they inherited the problem that's really going above and beyond what I expected.
I'll look at the driveshaft next as well as the motor and transmission mounts. Might as well check the rear subframe too.
Back in my BMW days it wasn't uncommon to destroy the "Guibo" (rubber flex coupling between the transmission and driveshaft) if beating on it. Perhaps I should check that as it can cause some vibration if distorted at all.
I'd be a little surprised if it were but it's easy to check.
So until I get home and can look at things closely that's where it stands.
It does not surprise me that you are feeling a vibration with road force values of 17 to 26. That is mighty high for a (relatively) tightly sprung coupe.
Many cars such as Mazda Miata's require single digit road force figures to drive shimmy free.
Assuming the road force operator knew what he was doing (often overlooked), and the machine was freshly calibrated, I blame your tires for not being "round" enough for your Mustang.
Have you had the tire beads broken loose to check that there is nothing in the tire? As in, maybe debris or tire lube moving around inside the tire where there should only be air?