In connecting a cartridge in balanced mode, to a balanced phono stage, ground is left to "float". As you know, the cartridge has no ground connection, per se, except for a very few older designs, like (I think) old Decca cartridges, and those cannot be hooked up for balanced drive. The shield on the phono cable itself, if there is one, can be attached to phono stage ground lug, but I have three TTs operating in fully balanced mode, and in no case has it been necessary to ground anything to anything. I don't see any problem with Mitchell's wiring scheme, certainly not one that can account for the phenomenon. And it's not confusing.
Someone else very early on mentioned the Hall Sensor, which is very likely used in the drive system of the Yamaha, because it has a DC coreless motor. On my Kenwood L07D, also coreless and also DC, the Hall Sensor is fixed to the plinth surface under the platter, but there must also be a signalling device built on the underside of the platter itself that rotates with the platter and triggers the sensor if there is a speed error. It seems possible that in balanced mode the phono stage is picking up a signal from the cartridge, as the Hall component that is fastened to the platter rotates under the cartridge. This is causing an impulse from the cartridge to push the woofer in concert with TT speed. But why this happens only with platter mat and LP in place, I do not know.
One idea why the problem only occurs in balanced and not in SE mode might be that in the latter case, both channels ARE connected to audio ground, so maybe the signal never gets to be amplified to drive the woofers. It would be interesting to hook the output to a 'scope and see if one can detect the spurious signal on hot or ground in SE mode.