The birds seem to bleed out more completely when just their throats are slit, something about the heart still beating that makes them empty out better. I find it easier & neater to do it this way: I zip-tie their legs together, wrap a length of duct-tape once or twice around their bodies to hold their wings in place and hang them upside down from hooks on a metal frame, positioned over a lined garbage can. Then I grab their heads, pull to straighten their necks, and slice the veins on each side of the throat. I try to get a good deep cut that makes the blood come out in a stream, I do both sides so they will empty faster & more completely. I usually continue to hold their heads down for a minute or two until they finish thrashing, so they don't spatter blood all over the place, keeping them dripping into the garbage can. (I use a black liner so it doesn't look so ghoulish) By then they're mostly bled out, but I leave them hanging for several minutes more.
This way they're already tied & hanging, I don't have to chase them around the yard, they're not thrashing on the ground, they don't have to be stuffed into a cone, they're not leaving blood all over the grass. They're also easier to grab & dunk in the scalding water and re-hung to pluck. I cut off the heads & remove the tape before dunking.