I get this kind of cyclic rumbly noise when driving. Noise goes faster as speed increases. Very slight change from acceleration to coast. At first, I suspected rear tires. The noise seems to come from the rear pass. side, from my perspective in the driver's seat, anyway. My impression is the noise cycles are about the same as the tires rotational speed.
I raised the truck's rear wheels off the ground, and ran it up to about 60. I could hear a very slight rolling noise that sounded like parts moving. In other words, nothing unusual. Nothing visually unusual either, other than the rear tires look like they had been on the front originally from the wear pattern. I replaced the left rear wheel bearings, as there was some play. Bearings looked fine, and noise didn't change. I found nothing unusual when the differential was opened up. I reset the right side wheel bearing, per Ford specs. Hub spun smoothly. The only reason I didn't do a visual, is because I didn't have a new seal handy. No change in noise after test ride. I did an experiment yesterday. I put the trans in neutral when I knew I would have to stop. Noise virtually disappeared. This suggests to me the tires are not the issue.
This really only leaves a few options. Rear, transfer case, or transmission. The rear appeared fine when it was opened up. U-joints could cause noise, but the speed would be faster than the noise sounds like, I would suspect.
The right rear wheel bearing is still a possibility. I will change that this coming weekend.
Any thoughts out there?

 

These type noises can be hard to find .
But ,as per your explanation it points to tranny.

So when driving along on the go pedal you have noise ,when you let off the pedal does the noise diminish or stay constant? If it does diminish and you think the noise is in the rear ,I'd look at internal diff carrier bearings being noisey.

If the noise stays the same( no change)
Tires are usually the problem .
What kind of tires and are they stock size?

U-joints going bad will cause a vibration + noise

Center carrier bearing in the drive shaft will make a noise constant whether on the gas or not when starting to fail.

Let us know what you find
Rich

 

A: I'm hard pressed to really suspect tranny.

A: Barely noticeable difference when off the pedal.
Noise disappears if I shift to neutral and coast at any speed.

A: Michelin LTX, stock size. My first suspicion. See answer above.

A: Have experienced this issue, but doesn't strike me as such.

A: N/A. Don't have one.

 

Do you have ESOF? If so, maybe the hubs are engaged, spinning the driveshaft, creating the sound at the t-case. If no ESOF, check the hubs.

 

Manual transfer case and hubs. Just turned rotors and new pads this past weekend. Hubs are not locked.
When there was snow on the ground, I left the hubs locked in order to get up my driveway. I shifted T-case into 4WD, then back to 2WD when leaving the driveway. There was never any difference in the noise with the hubs locked or unlocked.

 

Does the noise go away if you touch your brakes while driving?

 

Doesn't seem to make any difference. You can hear the noise slow down with the truck speed, coasting or with the brakes.