I would love to get my hands on the schematics for this amp. Not quite sure what preamp tubes run on AC heater circuit. More than likely V6 may be an AC heated circuit. Some preamp tubes will have isolation issues or may be susceptible to cross over transients which causes pickup of hum or static like sounds from the AC supply. The Reverb tank by itself is an antennae. Because of the powder coating or paint of the metal enclosure, circuit ground is not complete. The suspension springs are grounded that attach to the enclosure but seems that the box may not be due to the thin insulating film of the paint or coating. I have removed the tank for inspection, it is as reported the same tank used in the Mark V and Mark IV as well as other amps. The only difference, there is not lid on the box. This in itself may also be part of the issue. Wood does not make for a good shield. Also there was no aluminum foil heat shield on the top surface of the head unit. Those that have the combo, you should not have much of an issue with the noise since the box is complete and sits much farther away from the power transformer.
It is also possible if you have leaky power tubes (power tubes will be AC heated) that may cause the electrical transient noise to be broadcast in the AC heater circuit. Only one tube can cause this issue. Heaters are basically resistive, but there is an associated inductance in the heater element. Triodes and or Pentodes have high capacitance as well as other impedances depending on small signal model. There are many factors that could contribute to the noise level, intensity, or signal degradation. There are volumes of books on this subject. It is next to impossible to condense such that it would make any sense. It would be easier to do the trial and error approach than to understand the physics of the devices and associated affects of electrical transients. Another source of the noise in audio equipment would be the rectifier diodes in the power supply. They are susceptible to damage in the event of no load conditions on the output, the high induced voltage could cause damage to the diodes. In short, noise issue may be related to improper shielding of the reverb tank (lack of signal ground) or related to typical transients (most likely tube related). A faraday box or shield surrounding the reverb tank would be one approach in attempt to reduce the associated noise issue. Wire mesh (chicken wire), metal screen, perforated sheet metal. once constructed, it cannot touch any part of the Reverb tank since it will be earth grounded to the chassis. Signal ground may not be the same as earth ground so to avoid any ground loops (which will add more problems) chassis grounding of the Faraday box or cage and not connected to the ground of the input signal would be best. I may make a project out of this and get a perforated aluminum sheet to make the faraday box and see if there is any difference.
That is really cool. I did not expect to see a tight fit on the chassis. I like the floating face plate too. Have you thought about placing the Mesa Logo on it or is that taboo at the moment. 
