“By using a bullpup design, the Kel-Tec has an eighteen and one-half inch barrel to keep the Feds happy...”
The bullpup design has been credited w/reducing “perceived recoil” by some authorities; although I am not aware of the physics that would support that statement.
I, too, like the idea of a high capacity pump shotgun for home defense ...less to go wrong when compared to an autoloader ...assuming there is no “operator error” such as “short stroking” the pump action. The relatively short overall length is also advantageous for CQB and weapons retention.
The physics are pretty simple. Bullpup designs lower the axis of the bore in relation to the stock, usually so the axis of the bore extends through the butt of the firearm. In more "conventional" designs, the axis of the bore is considerably above the butt. By changing the geometry, bullpup designs have the recoil forces, which are directed backward along the axis of the bore, pushing the shooter straight back. Conventional designs, with the axis above the butt, create a lever arm for angular momentum. Thus, some of the recoil is translated into muzzle flip.
Muzzle flip is perceived as greater recoil, in part because it throws the sights off of target, and shoves the stock into the cheek ( or face if you do not have a good cheek weld).