I would tape or tack up a large piece of poster paper and shoot at a dot in the center of it. Why? That way you can see what your whole pattern is doing and where it is centered. Trust me, not all shotguns throw the center of their patterns in direct light of sight down the barrel. With a small target like a can or even one of those sheet of paper sized turkey head targets it can be hard to determine if that's the case.

Am I correct that you say you are using a fixed full choke? By that you are saying that this gun does not have a screw in choke system that allows you to interchange different chokes. Then I would shoot Hevi-13 number 7's and see what they gave me on paper. You did not mention how long the barrel is but even from a pretty long barrel you will probably not get great patterns out of lead 4's or 5's and maybe not even 6's past 30 yards. Heavy 13 7's are lethal to 40 yards and are your best change to get 80 to 100 pellets inside a 10 inch circle out to 40 yards. If they won't give you a pattern that dense at 40 yards then I'd lose money betting that any lead shot or larger shot size would either.