I had exactly the same fault with a TDS3032B (Noise superimposed on the signal)
Initially I contacted Tektronix but they wanted over £1000 just to take a look so I decided to pull it apart and see what I could find.
Same pcb as the 54 but only 2 hybrid modules fitted of course.
Carried out the same tests but could find nothing so reassembled the scope.
I then found that by selecting bandwidth limit of 20Mhz or 150Mhz the fault did not show.
Switching back to Full BW and the fault was still there.
However I switched the bandwidth to 20 MHz and cycled the power and then reselected Full BW
Unbelievably the fault had gone
That was over a year ago and the fault has not come back (I did try some percussive maintenance to see if it was a poor joint etc but could not get the fault to come back).
May be worth a try
NOTE: I cannot remember the exact sequence I carried out but it was something like I describe above but it was definately the Bandwidth setting that I was changing.
Jerry