Spins can be interesting animals. Though predictable (when you know your aircraft) they are affected by w&b, control deflection, trim, and rigging.
Agreed, most aircraft take a turn or two to stabilize the turn rate. Relaxing back pressure can increase the turn rate. Aileron deflection also affects rotational rate. Opp aileron slows it some, into the spin increases it.
You can take the low dollar route to spin education by visiting a RC aircraft club. Find a well versed acro pilot and ask for a spin demo. If you find the right pilot he can talk you through his performance while demonstrating the effects of various control input changes as he transitions from upright, inverted, rudder reversals, knife edge (full aileron & opposite rudder), flat spins. Many on the same vertical descent. The relaxed elevator input technique can be demonstrated with snaps also.