I have some (untested) theories about the cause of the noise.
Everyone seems to experience a low pitch sound that pulses (ramps up and down) at a rate of once per second. I don't think simple fan vibration could cause this cycling behavior so consistently among units. Therefore, I speculate that the problem is that the fan speed control circuit is oscillating at a 1 Hz rate. It probably has a feedback control circuit for maintaining the fan speed at a predetermined value (rpm), but the feedback loop is underdamped, so it keeps overshooting and undershooting the target rpm at a rate equal to the corner frequency of the phase lock loop, i.e., 1 Hz. This causes a burst of DC voltage to the fan once per second, which causes an increase in vibration once per second.
There is no way to fix the above problem without modifying the fan control circuit; for example, by connecting the fan to a fixed voltage source.
However, another theory may be more useful: I believe everyone reports that the problem disappears when the back cover is removed. This suggests that the back cover is amplifying the fan's vibration, and that he fan noise itself would not be bothersome if this amplification by the back cover could be suppressed. Because the pitch is much lower than one would expect to be produced by a fan, I theorize that the low pitch sound we hear that pulses once per second is the natural resonance of the rear panel, not a frequency originally produced by the fan. In other words, the rear panel is acting like the membrane (skin) of a drum, and the fan vibration is transferring energy to the "drum", similar to hitting a real drum with a stick, which causes the "drum" (the rear panel) to vibrate at its natural resonant frequency.
If this theory is correct, a better approach to suppressing the pulsing sound would be to apply damping material to the rear panel. If it is possible to order a rear panel from Panasonic Parts, one could sandwich a thin Sorbothane sheet between the two rear panels to produce constrained layer damping. A simpler but less effective solution would be to apply Sorbothane sheets to a large area of the rear panel using a very thin adhesive. (Sorbothane recommends 3M #80.) Perhaps Sorbothane hemispheres with a self-adhesive back could be attached to the rear panel so that the tip of each hemisphere presses against the aluminum panel that the circuit boards are mounted on. The pressure ideally should be great enough to partially compress the hemispheres.