Dear Banquo, Your verbal description does not paint a picture I can remember from having been "inside" my own SP10 Mk2. Perhaps I will take a look to refresh my memory. In any case, it is a relief to know that you don't have any spindle or platter wobble.
Now you say you have no plinth, it is possible that the vibration you experience at start-up is normal, if it goes away within a few seconds. The high torque of the motor WILL cause the chassis to want to spin in the opposite direction from platter rotation. (Remember Newton's 3rd Law of Motion?) At turn-on, max torque is elicited until the platter moves off from rest. During that brief period, it is quite normal for the un-anchored chassis to vibrate irregularly. I don't know whether this is the complete explanation for your dilemma, but it certainly sounds like this normal phenomenon is playing a role. In my own case, my Mk2 acted like it could walk off the shelf, when I started it up prior to its installation into a plinth. I daresay the Mk3 might actually take off in that scenario. Try physically restraining the chassis, and tell us what happens then.
Now you say you have no plinth, it is possible that the vibration you experience at start-up is normal, if it goes away within a few seconds. The high torque of the motor WILL cause the chassis to want to spin in the opposite direction from platter rotation. (Remember Newton's 3rd Law of Motion?) At turn-on, max torque is elicited until the platter moves off from rest. During that brief period, it is quite normal for the un-anchored chassis to vibrate irregularly. I don't know whether this is the complete explanation for your dilemma, but it certainly sounds like this normal phenomenon is playing a role. In my own case, my Mk2 acted like it could walk off the shelf, when I started it up prior to its installation into a plinth. I daresay the Mk3 might actually take off in that scenario. Try physically restraining the chassis, and tell us what happens then.