I picked it up tonight. The noise is still there, the whole shop is stumped. I'm going to drive it for a week and take it back next weekend.
The new rotors (AC Delco) which I asked for were replaced. The LF caliper and bracket was replaced with new pads.
The front hubs were changed as well (under warranty).
I may throw it on jack stands next week if the weather co-operates and run it in 2 and 4 wheel drive to see if I can hear anything.
Thankfully I'm retired and I have nothing better to do. :D

Do you have a two piece rear drive shaft?

No just a regular drive shaft. The rear u-joint was replaced 2 years ago, the front one was o/k. It was checked as was the front axles.
It makes the noise in gear and neutral. I even got it up to speed put in neutral and shut the engine off. The noise never changed, it gets more pronounced when applying the brakes.

Does it have ABS? Either way, is there any feedback coming through the brake pedal?

Yes it has ABS
No feedback pedal is normal but noise constant especially when braking. It sounds like big knobby tires, with either summer or winter tires.

I had a noise, a slightly grinding and vibration noise, coming from mine when I drag the brakes gently coming down a hill. After about 20 min of it, gone, haven't heard it since. It been driven on the street and hwy for many months before. A small rock may have been stuck in the caliper because I once drove over a bunch of gravel on the ground from a cement truck in my Cayman. I was parked up hill so some of the small pebble must have kicked up, went into my caliper and made a grinding noise when brakes were applied. I couldn't believe it happened. It was such simple thing but how can a pebble get stuck from it kicking off the ground? Nuts. Yours is complete different problem. There are only so many things that turn and make weird noises?

Believe me it's annoying but knowing practically everything has been checked. I'm getting used to the noise. I'm taking it back next week and he's going to take another crack at it. I'd be o/k it it's something like what happened with your Cayman.

Sort of related, my daughters AWD Escape had a noise I coldn’t Locate. Took it to my small one bay family shop, they drove the car for 15 min, put it on their lift and looked at all the components with a thermal camera. Replaced the ‘hottest’ item. Seems all A OK now..................Good Luck

Rich

Thanks, I need it.

Have the lug nuts been tightened to specs?

Yes, I've swapped summer to winter tires and back. Torqued to 145 pounds.

I'll update next week when I take it back.

Just thinkin' Maybe.

Just did an F-150 where we replaced the guts in the differential. No difference. 45/50 mph the vibration started. No noise. Just shaking.

U-joints and they demonstrated nothing odd.

Bob
I was thinking the same thing. I'm going to ask them to check the front u-joint. The rear one was replaced 2 years ago. I'm even thinking the front axles.

It was freaky. No indication of slop.

Some guy from a serious speed shop customer knew says matter of fact, it's your U joints (based on symptoms). It was.

My mechanic is losing his mind over this. He did say he will find it, and I believe him. He's never let me down in 20 years.

Final update
 

Finally got the truck back today. It's finally fixed.
Mr. Merk was on the right track
Bob Kontak was correct.
The rear u-joint by the rear diff. was the cause of the noise.
It's unreal that the u-joint would carry a vibration from the back all the way to the front.
Both u-joints were replaced, the truck drives like normal.
Thanks to all that posted and offered suggestions.

It definitely sounded like a u-joint but you said they'd been checked. I was thinking maybe carrier bearing on a two-piece shaft. My crew cab has a big single aluminum shaft.

You nailed it, Mr. Merk. I just came face to face with the probable fix simply because it was thrust into my face by a better mechanic.

Everybody wins!

Sounds like the pro version of what many consumers do; something sounds out of whack on their vehicle at speed. So, instead of replicating the operating conditions, the owner or tech looks at the static vehicle and guesses what part could create a noise he doesn't hear, then goes on a spending spree. Many repair shops and all retail new car dealers sorta love that.

At some point in time, with repeatedly incorrect guesswork, someone (you) will tire of the guesstimates (or run out of repair funds) and either go elsewhere, up the volume on the stereo or yell at the wifie and/or dog. However, there's hope. Chances are, replacing random parts will eventually "fix" the cause of the complaint. :(

Ain't in your best interest to go that route.

Did your tech ever contemplate putting your vehicle onto a rolling road (e.g. dyno) to simulate the driving condition? With the car in "motion" he or his tech helper can lie prone and listen to the front end at 25 mph or whatever to at least pinpoint the noise source.

Sherwood

I'll try and keep it brief.
It all started when I was going to DIY the front brakes. I couldn't budge the front guide pins on the LF caliper. I gave up and put the wheel back on.
The noise started at that point. I kept telling my mechanic that point. In the end the u-joint was going bad at the same time. Bad coincidence.
I told him last week that I'd drive it and see what happens.
I put the rear on jack stands and jacked the rear axle so the angle of the rear wheels would be close if on the ground.
I put vehicle in drive and looked underneath. I saw the transfer case moving slightly back and forth.
I lowered truck and went on the highway. The noise was present but if I hit a dip in the road the pitch of the sound changed as the truck went up and down.
At that point I realized it's probably a u-joint. It must have been getting worse.
He replaced the rear one by the rear diff. that was the issue. It was installed less than 2 years ago.
The front one was also replaced.
I only paid for the front diff which was bad, it made god awful noised in 4wd.
All the other work including oil changes front hubs, and axle was free.
I've been with this indy shop for 20 years. I'm still going to use them.