I use the 3.5" 12ga Hevi Shot Mag Blend in an auto. (Rem SPR 453 aka Baikal Mp153) with a Carlson's .665 dia choke that combo I feel good with to at least 50 yards. I patterned it at 45 and I stopped counting the head and neck hits. I've never had occasion to shoot one farther than that (we can use rifles in SD) as it seems too easy. I'm sure with optics a guy could reach out and touch one at 60 with the 3.5 pretty easy.
I previously used a 3'' 12ga with Hevi 13 #6's which is also good at 40 but the pattern is no where close to the 3.5.
I shoot most of my turkeys under 20 yards at which distance Im sure you could use about whatever with a full choke and get it done. I know at 20 yards with that 3.5 it would bring a new meaning to "Jelly Head" if you centered it. Which is the main reason for the turkey chokes, a tight pattern results in less wounding.
Do you need a 3.5" 12 or 10ga with TSS or Hevi 13 to kill one? No way. Does it open up more opportunities for you provided you have patterned the gun and know where it hits farther out? Absolutely.
I use archery tackle most of the time. Closest ever kill was around 8 yards with a bow, farthest was about 40 yards with my 3.5" 12 and Hevi 13 Magnum Blend. Only time I have seen a turkey backflip shot with a shotgun. The rest have all been 20yards and under and dropped at the shot.
