Remington themselves offered two choke tubes that stuck out beyond the end of the barrel. One was called an extended full and the other called a Turkey full. I have both, both are very good. The Turkey full has a knurled end on it for quick hand removal. It is my choke of choice if I had to pick only one.
I have an HS Strut Undertaker choke, they retail for about $20 at Cabela's. It's an extended screw in and does me well. The picture that I'm attaching I took after I patterned the gun 5 years ago. To put my hunting skill at that time into perspective, I had to start a thread on a site for Geezer to tell me how to take out the choke tube! So it's not the best pattern (as in, aimed on the paper) but every bird I've shot at and a handful of other things have always died. I use Remington Nitro #4's in 3 inch and I don't like to shoot them very much.
Just use a factory full and get good shells. if you don't kill em out to 40 yds it ain't the guns fault. super dooper tight patterns are great for long shots but most turkeys get shot under 30 yds....I bet for every bird killed at 50 because of a super tight pattern there is one missed at 15 for the same reason.
I have used 3.5" 12 gauges for turkey hunting for awhile and they will reach out. I haven't killed a longe range bird with my current setup that I have hunted the last 2 yrs with ( Beretta Extrema2, fact full, 3.5" Winchester HD number 5's) but my last setup that I toated for 12 yrs was a 835 and I shot 3.5" federal lead 5's...Killed several birds wayyy out there with it. One I shoulda never shot at was 64 paces....I shot it running after my buddy made his strutting mate flop at 30 yds...Killed a couple others at 50ish yds after other people missed em closer.
The first turkey I slayed with it was at 7 yards...so close I almost missed because the pattern was so tight! The second was my big gobbler and he was out to about 30 yards. I would shoot to beyond that but probably not to 40. When I set up my decoys and am calling, ideally (which, of course, never happens) the places I hunt in, I see most of my shots being in the 15-25 yard range