Oimophysics uses Inertia about center of shape at (0,H/2,0) assuming origin at center of base of shape.
While calculating Inertia of body, parallel axis theorem is used but I think cone geometry should be treated differently as its center of mass lies at (0,H/4,0) rather than (0,H/2,0).
Correct me If I misunderstood your method of calculating inertia tensor.