Nice lathe work!
The key to a flip over top is the balance point must be very low. Notice that your top leans over when stopped. A flip over top will rest with the stem straight up. 2 ways to do this are: A thinner finger stem to make less weight up high, Or adding metal to the bottom. (top after flipping)
The outer surface should be a sphere. I do not know how accurate the sphere needs to be.
Kirk