I had a weight fall off the driveshaft and wheel once. Might want to check and see if this happened to you. You could also remove the rear brake drums and look to see if they were clocked differently when installed by using different lug holes. This will change the balance some. You should see rusty circle on the drum that aligns up with the access hole in the axle flange.
I think I've asked this before but not sure, so I'll ask again. What is the correct orientation of the access hole in the axle flange to the large weight on the brake drum? Any correlation?
The weight could be anywhere on the drum that Ford needed it to be to balance the whole rotating assembly (axle/drum)
I'm going to guess that there were no vibration problems after the balance job was done. If the new vibration goes away when you let off the gas, I would suspect something related to the drive shaft. 1 slip yoke bushing it tail housing of trans. 2 u-joint (over tightened u-bolts can wipe out the rear u-joint in a short time) 3 pinion bearings I would start with the rear u-joint, remove the u-bolts and spin the caps and see how they feel.
does it feel like a rotational vibration? if so and you feel it through the seat it could be the harmonic balancer, drive shaft balance or when this happened in my car it ended up being the wrong weight flexplate.
I may be wet here but in 45 odd years of vehicle ownership I've never heard the axle & drum were balanced as a assembly, never... It doesn't make any sense, what is one going to do if they need to replace a drum??? Anyway I've always just "tossed" them on after knocking the dust out, never remember having a issue...
Back in the day the factory used what was called mass balancing. This is why you see paint dabs on the driveshaft and rear end yoke so you will know how to put things back where you got it when put it back together. Same goes for the brake drum. I'm sure you're old enough to remember tires being spin balanced were better than bubble balanced. Mass balance works on the same principle as spin balance.
Right now, I'm going to try to find a "decent" harmonic balancer under $100 to see if that fixes the vibration I feel in park and then see what it feels like going down the highway to see if there's any improvement. It would be nice if it was just exhaust drone, but I don't know for sure. That balancer replacement is next for sure though. Thinking about that Summit balancer for around $80 instead of the same money at O'Reilly for a Dorman.
If the vibration is there when running the engine in neutral the problem can't be any further back than the torque converter...