NB: Edited the text below to make it clearer and add the effect on AMI.
I have no experience with throwing tops. How does the top's curvature affect its play -- not just in theory, but in practice? (By "curvature" here, I mean the curvature of the top's silhouette in a plane containing its "axis" of symmetry.)
For example, let z track "height" along the axis, and r(z), the perpendicular "radius" from the axis to the silhouette at height z. Then the silhouette is just a graph of r(z) vs. z. If T(z) tracks string tension at the top as the string leaves height z, then the driving axial torque Qd(z) applied to the top grows with radius:
Qd(z) = T(z) r(z)
Hence the silhouette shapes the driving torque curve Qd(z), which in turn limits release speed. The aerodynamic braking torque Qa(z) opposing the driving torque also grows with r(z), but at an even faster rate. Hence the net axial torque (ignoring tip friction) at height z during spin-up is
Q(z) = Qd(z) - Qa(r(z)) = T(z) R(z) - Qa(z)
To accelerate the top to release speed, this net torque has to work against the top's axial moment of inertia (AMI), which depends on the shape of r(z) and grows very roughly with the square of mean radius.
When integrated over the appropriate height range, are any of the net effects noticeable in play?