I wonder if putting the car up on four axle stands and then 'driving' the car with and without the rear wheels would shed any light on the cause. (but do make sure it cannot drop off the stands!!)
I'm guessing that if it is propshaft induced it will still vibrate without the rear wheels fitted.
I know I joked about flat spotting your tyres but maybe if the car has been sitting on the old tyres for a long time then maybe they have deformed?
My bet is on your old wheels or tyres...........
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