I grew up in one of these game units. It was a shotgun only unit. Unfortunately, a steel slug in a shotgun would permanently damage the shotgun because steel does not give the way lead does. A shotgun has a choke which reduces the barrel diameter toward the end of the barrel. There are sophisticated ways around this problem such a sabot loads but this begins to make the shotgun perform more like a rifle defeating the entire purpose.

I was persuaded enough by the research that I decided to move away from lead slugs a few years ago. I currently use these steel slugs for deer when required to use a shotgun, and find them extremely effective: https://www.ddupleks-usa.com/broadhead-hexolit-32. I'd recommend checking them out. Like most ammo, availability is spotty right now, but cost is reasonable when they can be found.

This is an interesting ammunition. A sabot for sure but the flat/concave face keeps it out of the shotgun acting like a rifle scenario. Thank you for directing me to this.