I understand running over a mattress can cause a vibration.
The last drives haft I had balanced made a wonderful difference in the entire vehicle at almost any rpm. I watched him heat a little spot the size of a quarter, get it to straw colored, quench it with a wet rag, and then look for the next GRAM to work out of it.
I'm having a bit of doubt about shavings causing vibration. Vibration may have caused shavings though.
If it's the rear end I'd have noticed, I'm pretty sure, a difference in loaded and unloaded rear end(accelerating, decelerating, coasting) and probably a difference in making a right turn versus a left.
I'd sure get a second(and then some) opinion, and/or a guaranteed in writing money back if this is just a
'we think this'
And they aren't even close to right.
I have sincere doubts about their diagnosis.
Lots of rear end things can do this, pinion wise.
Shavings are a sign, not a cause.
As said above, by Beau who has a HUGE knowledge base:
It might just be the harmonics of it all, and I'll add to his perfect reasoning: the people telling you of it has triggered your awareness.
I'd sure bet on that.
My 70 1/2 z28 LT1 350 hit resonance and was VERY noticeable. Solid motor and trans Mounts made the whole car kinda have a not so subliminal hula roll to it. It happened at I think 2150 rpm... At exactly 55mph back in 55 mph days.
This is for sure one of those:
Until it's bad enough, or your mechanics diagnosis skills are good enough, leave it alone until it can DEFINITELY be diagnosed.
A differential is not a thing you want a dealership
Read, remove, replace type mechanic touching.
He changed a headlight yesterday and will work on your rear end tomorrow.
Go to an offroad shop and have them look at it.
A dealership will change 3 diffs a year on the far outside guess and maybe only 1 in 3 years, but an offroad shop does 5 drive lines a week.
As said above, a dealer can sure make it worse.
Jack of all master of none, or a specialist.
Choose the specialist.
Your differential, once out of warranty, should have nothing ever ever to do with a Ford dealership mechanic.