It's far more likely to have been the "equal and opposite" reaction to the ejection seat departing shoving the nose down that solved the spin. Shifting the CG aft won't improve your chances of departing from a flat spin. Various airframe designs have corner cases that they can't escape normally - delta wings are a bit prone to a flat spin, and you can get a T-tailed configuration into a "deep stall" where the disrupted airflow from the wings is blanketing the tail such that you cannot get the nose down with aerodynamic controls. The correct action is to avoid entering such conditions.

A rocket blasting off from the nose, meanwhile, is not subject to the same constraints, and will force the nose down enough that the plane can obviously, in at least a few conditions, recover controlled flight.