My thoughts.

1. Lack of penetration is definitely due to poor slug construction/soft lead (ie winchester and remington). This article while for the 410 ga gives a good description. http://mcb-homis.com/deer9410/index.htm
At 40 yards a 16ga 4/5oz or 1oz slug should kill a whitetail 100% of the time if the vitals are hit. I would recommend Brenneke slugs since they are hard, accurate, and penetrate well.

2. There is no reason not to shoot slugs in that gun, none. All shotguns after 1934 I believe are built to withstand a certain max average pressure. In the case of the 16ga that is 11,500psi. So the gun if it is in decent condition will handle the pressure of ALL factory or published reload recipe loads.

3. All factory 16 ga slugs are designed to be safely used in barrel choke full (~.035) or less. In the case of the poly choke you should set it to cylinder and work up until you achieve the smallest group.