Ballistic Products makes a slug and wad combo for dangerous game for the 16ga. Measure your actual bore diameter and then see if a slug will pass through without much compression. Or, have a ball of the size of most constriction with under wads or one that will fit in a shortened shot cup that will fit the choke including the wad wall thickness. Now, powder charges are an issue. I use Black powder loads and fiber wads (or black powder substitutes, I like the goex one and have used Hogdon 777).
You can get some charge and wad combos from Ballistics.