That's awfully far for a shotgun...I don't know how much energy those slugs are packing out there but it sounds like you know it works since you pass up shots a couple dozen yards further out. It's good to have a max range in mind.
Yes, an Encore is capable of the shot you want. A 250gr or 200gr Shockwave in front of 80+ grains (the more with accuracy the better) of T7 powder will do the trick. Be sure you know your exact range though, bullets tend to drop awfully fast out there.
So the gun will do the trick, just be sure you go through a few boxes of bullets to make sure the shooter can do it justice UNDER FIELD CONDITIONS. Four inch groups off a bench usually turn into at least 8 inch groups in the field. You'll need, at minimum, shooting sticks or a good bipod. I'm a fan of a Harris tall bipod mounted directly to the forearm.
