I reach underneath them, and grab one leg, then the other, from behind the turkey, moving deliberately and calmly but FAST - and carry them upside down where ever I need to go with them.  The little girl that raises them for us taught me that 
  Apparently, when they show them, they hold them upside down like that for the judges....I have NO IDEA how you would catch a faster turkey like a heritage breed!   But those BBW turkeys are like pets with that girl...and fat and slower than a heritage turkey...My motivation is if a 13 year old can do it, I can do it 
  
I usually just go in while they are standing to tie up their legs, corner 'em again, and use the left over bailing twine from hay...as long as they aren't bigger than a bag of feed, I'm okay.  We got some toms from her one time that were HUGE and it took my husband AND myself to get them processed...but since then nothings has been over 40 lbs dressed either....now they call us as soon as they are done showing, which helps.
When I weigh them, I either use a hanging scale we have once they are tied up - or if I am just going for a weight I do the "showmans hold" the girl taught me and stand up there with the bird, weigh us together, then deducted me weight alone....I never try to hang on to one like a football...always sneak in for the legs like she taught me...that way they can flap all they want, but can't get me!
One other thing, I don't know that it's true, but they also taught us not to lay them on their backs - said it stressed them - but if I HAVE to since I am going to process immediately, I will lay an uncooperative one on it's back so it can't flap it's wings at me...then straight to the gallows it goes...I had one feisty mean one this time - the very last one I processed, so I'm sure that turkey hen had it figured out....she had to be caught, flipped belly up, tied and then hung for the kill...I felt bad...but I wasn't getting wacked in the face by a wing....and you could tell she was having a hard time breathing once I got her flipped over on her back, so I moved as quick as I could.
My husband reserves shooting for anything we CAN'T CATCH - run away roosters, deer....if a roo gets loose and is destined for freezer camp and we CANNOT catch it, he'll sit patiently and wait for a head shot.  But he HATES to waste ammo on domestic things - even the meat rabbits, we don't shoot those.  He says it's like "hunting at the zoo and is just a waste"...I kinda see his point....