Free: Contests & Raffles.
Depends on what your Stoeger is choked. Others may disagree but I do not fire hard slugs, out of anything tighter than a cylinder bore choke. As your Stoeger is not rifled it would also not be any advantage to fire a "rifled" slug from a smooth bore barrel. You might want to think about a Brenneke slug for such use.
I've shot 10+ deer with a 12 ga smooth bore and 2 3/4" slugs, usually shoot Winchester super x but those are hard to find around where I have been looking so I have tested some Federal blue box 2 3/4" and they group fine and are fairly cheap. You can bat cleanup well out to a hundred yards with those no problem. If you don't try to hit the shoulder there is very little meat loss, similar to an lung shot with an arrow.
I've shot at least ten deer with buck shot and not lost one . typically guys loose them because the areas they hunt are brushy as hell and they cant or wont follow up. I used to hunt with a mossburg 500 with a 20 inch open choke barrel and 00 buck it was deadly out to fifty yards , when I threw a slugger scoped barrel on it my effective range with slugs increased but I lost that quick close range effectiveness .