I've been experiencing some vibration or roughness when driving at any speed. I've been unsuccessful in diagnosing the problem. The vibration hits a slight harmonic at about 60 MPH. It feels somewhat like an unbalanced tire or a like it feels when you drive across heavily grooved pavement on the highway.

Possibilities I considered:
-Wheels out of balance (tried rotating wheels, no change)
-Universal joint (jacked up rear of car, put in park, and tried rotating drive shaft by hand - does not seem to have any play across joint)
-Transmission problems as described in other postings (I hope not!)
-Engine mounts (all three look OK, best I can tell. Also put car in gear, held brake, and sped up motor in fwd and reverse, and saw some engine movement, but does not seem excessive)
-Ignition system (no fault codes received, pulled, inspected plugs, coils, wires, all look OK)

Based on other posts, I tried manually changing gears while at highway speeds. The vibration seems to change with the engine speed, not the wheel speed, so I think the problem is not with the wheels, drive shaft, or transmission. I also think I can hear some of the roughness if I rev the engine while in Park.

Whatever it is, it does not set off the check engine codes.

Any suggestions on what I should check?