Talking just about models and not full scale. What you have is the airplane at 60-80 degrees angle of attack with a really big yaw rate. Think about how a modern model that does 3D maneuvers is flying. They can be fly (although the surfaces are fully stalled they still create lift along with a boat load of drag) and be controllable at 60-80 degrees angle of attack using just the prop blast over the tail surfaces. This includes roll, pitch and yaw. The ailerons are usually full span and the tail surfaces are big. Since the prop blast is all you have to work with (well almost) they have to be big.

Now think about the Hog. It has small full strip ailerons and relatively small moveable tail surfaces. However a good prop blast across the surfaces that are there will help. You can use the ailerons deflected into the spin direction to roll the airplane. Although you use the deflection to help get the rates up to enter the flat spin it also changes the angle of attack to a sideslip angle as the airplane rolles about the airplane body axis, reducing the airplane angle of attack and increasing the sideslip angle. The directional stability is more effective in recovery and full down elevator in the prop blast and rull rudder opposite the yaw rate will give a nose now and anti spin moment.

You end up with an airplane going to a lower angle of attack where the vertical tail and rudder is more effective and it will literally roll out of the spin. It does require a good prop blast though.

Whether or not the airplane will stay in a spin depends a lot on the directional stability of the airplane, Cnbeta, yawing moment with respect to sideslip angle. I had a shoulder wing model (bought from a friend that built better than I did) with what looked to me like a small vertical tail. It flew nicely though and would spin and flat spin on command. I thought I would dress it up with a canopy right over the wing. The CG was the same since the canopy was right over it and the weight was the same (just a piece of very thin plastic). The canopy lowered the Cnbeta of the airplane and the next time I tried the flat spin it would not come out. The ailerons were conventional located and could not get any prop blast over them. A landing in high weeds next to the field saved the airplane.

I removed the canopy and things were back to normal. The extra area forward of the vertical tial lowered the Cnbeta. The change wasn't much, but enough.

The same thing happens with a CG change. The Cnbeta is lower with an aft CG and the rudder moment arm is lower which will keep you in the flat spin. Go forward with the CG and both items change to a favorable value to let the airplane pull out.

Full sized airplanes are a different horse, as some of the writers noted the inertial effects of the prop are significant where as our relatively little (with respect to the airframe) props don't do much in that regard. Perhaps a geared electric power plant turning a really big prop would act similiar to their larger brothers.