Lots of SP10 Mk3 users have removed the motor assembly from the base chassis and re-installed the motor only in a plinth that permits the coupling you describe. I have nearly achieved the same thing without doing that in my home made plinth, but I do wish I had had the guts to just pull the motor. Steve Dobbins was the first to do it commercially and make a plinth to go with. But this is a sidebar to the question at hand.
Albert Porter's Panzerholz re-plinth does not involve removing the motor assembly from the square chassis. So his plinth is certainly superior to the Technics plinths made for the SP10 Mk2 or Mk3 but is still subject to the issue of which you speak. He deals with that by installing a block of solid iron below the TT. There is a threaded rod (steel or whatever) that screws into the iron block and is adjusted to fit snugly up against the base of the bearing housing. The block is firmly coupled to the chassis, as is the tonearm. I've done the same thing in my home made slate and cherrywood plinth, but I used brass instead of iron; I did not like the idea of installing such a massive piece of iron so close to the permanent magnet that constitutes the rotor of the motor.