You missed 'cause your sights were off, not 'cause of a choke to tight. Trying to reverse engineer a system that is not correct to start (a loose enough choke to make up for sighting errors) is backwards logic. Zero the sights, do not play games with choke.
Were the gun "on", and all else right, you'd have a dead gobbler, irregardless of choke. A true turkey gun is a specialized tool, short, tightly choked and with good sights to allow delivering heavey payload into dense patterns to 40 yards or so. Turkey gun sights need to be adjustable and tough. Once on, they should take all manner of reasonable use and some abuse and not need fuss or worry. Old school turkey guns, with their looser full chokes and bead sights were OK, (sloppily compatible?) with beads, to an extent, but give up some range to the "new wave" guns. Today's specialized guns, with super tight chokes and dense special purpose loads, need sights.
Too, make an effort to shoot at a gobbler by holding at about the wattles, (center of neck) not holdding " on" the head. A head hold will throw half your shot charge over the tom, everytime, with everything being perfect. You basically give away half your payload, and are relying on only the "bottom" half of the pattern to do the killling. A gobblers head is pretty animated and articulated, always moving and searching. A head bob at close range at the moment of the shot, and a high "head only" hold, maybe some brush to strip the pattern, and you have all the makings of an educated and safer gobbler and one heart broken gobbler hunter. (ask me how I know).
For me, I want the added reach and clout of a dense pattern. A good sighting system, hold understanding, and a cool head (well 2 out of 3 anyhow) gets me more gobblers. I do not want to give up ten yards of reach for a few inches of slop at close range I should not need.
While I'm at it....I started hunting a combo this year that has real potential, a short barreled full and modified choked over under. The full barrel shoots extra full with premium ammo. The Mod barrel is about old school full with same. With the same load, I can "dial in" the choke I want at the time of the shot. (the gun has single/selective safety. Over dekes from a blind at ambush and close range setups, I can use the mod ( old school full) bottom barrel. In open hardwoods and roaming, I can use the full (extra full) barrel for the bird that hangs up at 40 yds and will not budge.
Just need better sights and a sling rig.