I'd start with some 3" loads if your gun is chambered for the longer shell. Skip #4 and #5 lead and stick with #6 or even #7.5's. This will help increase your pattern density because your pattern will run out well before the pellets run out of enough energy to penetrate Mr.Gobbler's vitals.
For example, 1 ounce of #6 lead will contain roughly 225 pellets. An 11/16 ounce load of #6 shot from a .410 will contain roughly 154 pellets. (225 pellets/ 16= 14 pellets per sixteenth X 11 sixteenths= 154 pellets)
11/16 of #7.5 lead will contain 240 pellets, (350 per ounce divided by 16= 22 pellets per sixteenth X 11 sixteenth's= 240 pellets). This would be the optimal choice since you have more pellets to deal with, and they still pack enough punch at 20 yards to kill a Turkey.
Pattern at 20 yards and see if you can put 100 pellets (minimum) in a 10" circle.
By way of example, a 1 ounce load of #4 lead contains roughly 135 pellets. An 11/16 ounce load of #4 lead will contain roughly 92 pellets. That means you're under the 100 pellet threshold before the shot column has even left the barrel. Move 20 yards downrange and it only gets worse.
Long story short, a .410 is capable of taking a Turkey if you use smaller shot, and close range. Just a guess, but from prior experience with my fixed choke .410, I wouldn't take a shot any further than 25 yards... and that's probably pushing it.