Your description of the motor vibrating is very much my situation too. In fact I've found that any of the methods where the motor and bracket are allowed to vibrate freely, no matter what kind of suspended mounting, sorbothane grommets, blu-tack, etc., results in more resonant noise than firmly securing the bracket with transit screws. Adding blu-tack between the bracket and the plinth when screwing it down seems to help dampen and direct resonance transmitted from the motor, but it's still there. My motor vibrates quite a bit when I hold it and also does not turn smoothly when I turn the spindle manually. I actually just ordered a new stylus for my cartridge and will be talking to my dealer when I pick it up, so I may price a new motor at that time.
So I'm curious to hear how your motor change turns out.