Even if you find the best-shooting slug or round ball in your shotgun, at that point it's still no more than a musket (in terms of accuracy). My country was liberated from the most powerful nation on Earth at the time (depending on muskets) by a relative handful of RIFLEmen picking musketeers off at rifle distances.
Arrows through a smoothbore can be surprisingly accurate at distances that balls or slugs are shooting patterns, rather than groups. Not that it matters for your application, but that Wing Shot is easily capable of taking any game on Earth... with arrows.