Well...I am gonna argue with that a bit, if you don't mind.
A - the singles from H&R/NEF really don't fit into this discussion.
B - when one takes a full length stock off a gun, as well as a few inches of barrel, a substantial amount of weight has been removed. In my book, anything under seven pounds is a lightweight SG..YMMV.
C - Having never shot a Shorty, I have no first hand experience. I do know that recoil is a function of weight (of shot, powder, gun) and velocity. Given the same powder and shot stats for both a SS at 4lbs and a FL SG at seven pounds (most FL SGs weigh more than this) reducing the velocity to 900 fps for the SS (from 1200 for the FL SG) the recoil of the small gun is actually more that the FL gun. At 850 fps, they are the same. Of course, I am only guessing at the SS velocity. (Does anyone know what the velocity is out of 6.5" bbl.?)
The point of this set of data is that PGOs do have more recoil....they weigh less than the same gun with a longer barrel and longer stock. Lighter guns have more recoil, all other factors being the same. They would have to lose a whole lot of velocity for that to change.
The weight difference between a Mossberg Persuader/Cruiser when going from FS to PGO is one pound and a 16% increase in free recoil.