Every shotgun is a bit of an entity unto itself. Two shotguns, both the same exact model, are not guaranteed to shoot equal patterns even if you use the same shells and chokes in each. So it's impossible to promise you that a certain shell and choke combo will be best in your gun. Unfortunately it takes some money and range time to find what's best for your gun.

That said here is my two cents worth.

Start with denser than lead shot. Denser than lead shot will out pattern lead shot of the same size by a wide margin. For me this this the primary reason to switch to DTL shot before even discussing how much better it penetrates. But of course it penetrates better as well. I hear people talk about amazing patterns they get with lead. Some even claim great patterns to 50 yards. (Mostly I hear this on the internet) Not calling anyone a lie but I'd have to see a good laser ranged 50 yard lead pattern fired in my presence before I would believe it. Never seen one in person in 15 years of seriously testing multiple shotguns, chokes and shells belonging to me and half a dozen friends. And we are talking at least 9 different types of shotguns, at least 20 different types of chokes and lord knows how many different kinds of shells. Spent more money than I care to try an add up. I call a good pattern at least 100 pellets inside a 10 inch circle. In all my years I never found a shotgun/choke combo that would consistently meet that minimum standard with lead 4's or 5's at 40 yards much less 50. I found one load of lead 6's that would do it but lead 6's start running out of steam fast at 35 to 40 yards. A shotgun that will consistently put 100 lead number 5 pellets inside 10 inches at 50 yards is as rare as a unicorn. If it even exists at all, which I doubt.

Try some Hevi-13 6's or some Hevi-13 Magblends. I promise they will pattern way better than any lead shell. Also there is "ABSOLUTELY NO REASON TO SHOOT ANY SHOT SIZE BIGGER THAN 6's WITH DENSER THAN LEAD SHOT". The 6's in Hevi-13 will kill turkeys as far as your gun will hold a killing pattern. And they will pattern way better than the 5's or 4's. So it is senseless to shoot the Hevi-13 4's or 5's.

As for chokes? Indian Creek BDS, Rhino, Pure Gold, and the new Hevishot chokes are the ones I have had the best luck with in my 835. But as said before which of those would be best in your individual gun is impossible to say. But one of those paired with some Hevi-13 will stomp a mudhole in any lead shells @$$.

To evaluate each shell/choke fairly clean your gun in between shots. And shoot at a big sheet of paper so you can see what your whole pattern is doing. Forget the turkey head targets unless you are going to tape them to the center of a big sheet of paper.

If you really want to get hardcore about it look up how to give the inside of your guns barrel a good polishing. It will improve patterns by as much as 20% in some cases.