I believe the equations for spin rate are related to the mass moment of intertia as noted. It is a function of mass times distance from the axis squared.

The spin velocity is a function of inputs due to aero moments and forces and the mass times distance squared (some liberties have been taken because I can't remember them all!) As the elevator drives the angle of attack down the distance from the spin axis of mass get lower, the answer is lowered by a function of squared numbers and the aero forces and moments haven't chanced all that much. So you get a faster spin.