I've spent a couple hours looking at search results here. I just bought a November 2015 production F150 SC 2WD XLT 3.5L. It has a vibration coming from the rear (don't feel it in the steering at all) that starts to be noticeable about 45 mph. It gets worse up to about 70 MPH, then gets less bad until it isn't noticeable above 85. It is worse under acceleration and deceleration than neutral throttle, particularly at higher speeds. This makes me think it isn't wheels or tires, or at least not all wheels/tires.

13k miles ago there was a cryptic "transmission and drivetrain diagnostics" entry in the the maintenance log, with "changed plenum gasket" as the resolution. The transmission fluid was last changed 60k miles ago. The tires were new 35k miles ago. It was ~22 oz low (out of 176 fill capacity) on differential fluid when I bought it. Seems to be no play in the center bearing or u-joints.

I'll swap a spare set of wheels and tires on to see if that's part of the issue, but it's clearly not all of it since it is somewhat throttle position dependent. I need to check the pinion angles. I'm thinking I'll change the trans fluid and filter, even though my symptoms don't exactly match people who found that to be a solution. Suggestions?