Yeah, a prop has an effect similar to vertical (or horizontal) area, but only when it's running. The reason for this is that anything that deflects airflow creates 'lift'. Deflecting airflow to create lift is most often thought of as something done with a wing but the inflow of air into a prop disk is also deflected by the spinning prop. This effects longitudinal as well as directional stability.
The precise math is beyond me but the effect is basically proportional to the thrust the prop generates. When creating no thrust there is no 'area effect'. So as you found; pusher props mounted aft of the CG are stabilising but tractor props mounted ahead of the CG are de-stabilising (while they are running). Cut the power and the effect goes away so it's a risky business to reduce fin area and rely on the stabilising effect of a pusher prop to 'top-up' stability.
Tractor installations are (from what I've read) usually thought of as more efficient overall, for most applications.