It isn't considered humane to bleed them to death without first stunning them, hence the distaste for halal and kosher slaughter. Stun first.
Catching up after they are roosting is easiest, hold them firmly and tie up legs before turning them upside down as it'll be less stressful. Put their head on a hard surface like a low wall or the floor if not soft. Stun by either hitting them very hard on the back of the head with a blunt instrument like the back of an axe or shoot through the top of the head with an airgun whilst in the same position and then cut the jugular which means cutting deep enough to get right back to the spine and hang up to bleed for about 20 minutes.
Alternatively, rather than stunning, use the broomstick method. Turn the turkey upside down, down the length of your legs with its feet facing you. Put the head and start of the neck on the ground so the throat is in the ground. Put a broomstick across the neck right at the back of the skull, stand on broomstick both sides of the turkey and pull upwards firmly and hard. That will dislocate the neck (you can feel it disengage) and the bird should bleed into the neck cavity so far less messy. If you pull too hard though the head comes right off which isn't nice. I prefer to completely decapitate mine afterwards anyway just to be certain they are dead.
Be warned though: whatever method you use, they flap like mad as they die and they take a lot of holding. If they flap freely, they can end up bruising the meat.
Ten days is an ideal time to hang turkeys if you can keep them somewhere cool enough.