Okay, here's a true story:
I was turkey hunting in Nebraska, I'm at the end of the shelterbelt (a long row of trees planted for a windbreak) and my uncle is at the other end. I hear him open up, and knowing his shooting abilities, get ready for turkeys to come by me. Sure enough, a whole flock (fall season, hens are legal). I shoot once, but my swing catches a cedar. Shoot the second barrel of my over and under, turkey is flopping the rest jump the fence. I run up on two birds left behind, grab the livleiest one...wait a minute, I shot twice, missed once so where did this one...All Hell breaks loose. This jake (about 14 pounds) had gotten hung up in the hog wire fence and couldn't back out before I got there. He's 100% healthy, and luckily his spurs are still nubs, but his toenails dig in to my gut. I get worked over really good by the wing joints, hitting my nose. Not hard like a punch, but brings tear to your eyes and knocks the snot loose. It also sent my eyeglasses flying. The flight feathers actually cut my face a couple of times. I can't get disengaged enough to give him a good swing to break his neck (think of the jerk of a hangman's noose), so I pin it to the ground with my knees and use my Gerber LST pocket knife to pith it like a frog in biology class.
My uncle watched this whole fiasco. He said it's a good thing I won by a knockout, because the bird won all the early rounds.
Other guys have leopard stories, charges by elephant or Cape Buffalo, Grizzly Bear run ins...I have a turkey story. It isn't even a 20 pounder.
Oh, so how best to dispatch a turkey? If in doubt it will run or fly, definitely shoot it again. If you roll a turkey and the head pops up, you definitely shoot again, because it's gonna be heading out. If the head is down and it is fluttering, get over there as quickly as possible, and if it is alive grab it by the neck, give it a good swing, and then jerk back the opposite direction, and it snaps its neck.