I'm not sure that it is the gearing, but the changing of the clutch seems to be what causes the vibrations. Does it only shake when you have a load on the motor? What happens if you put the minibike on something to get the wheels off the ground, and then you twist the throttle? Does it vibrate in the same way? Does it only vibrate when you're riding it? Stick a 4x4 (or something that will lift the rear up so that the wheel doesn't touch) under the frame rails to lift the rear wheel off of the ground and sit on the bike. be careful not to wind the motor up too high, but note the level of vibration. Is it similar to what you see when riding it? If so, I don't think it is the gearing. If not, then I would say that it is possible that the gearing is what is making it vibrate.
What rear sprocket are you running? Is it the kind that allows you to swap sprocket easily (similar to those on racing karts)?
If I were you, I'd keep a notebook in the garage. Write all of this down and look for patterns. This is how you build your knowledge base. Experience is a great teacher. As you tinker with this thing, you'll learn a lot. Keep information on the performance of your engines as well. If I remember right, you've been posting a lot about the build up of your engine. Write down what you've done, and what you've seen. When you build the next motor, take note of what you've done differently and how that has affected the performance. This experience will be very beneficial.