Well, I'm presuming that other folks more knowledgeable in chicken anatomy & physiology have determined that if those particular vessels are severed then the bird is rendered instantly lifeless, and there is a logical explanation for the continuation of movement. I'm taking their word for it, and not feeling guilty when the birds I dispatch by throat-cutting continue to move while they bleed.
They seem to do the same amount of movement after getting their heads chopped, the only difference is that you know for certain they're not really feeling any pain.
That's the reason I stopped doing the yank method, because I couldn't tell if they were continuing to flap out of protest or just reflex. And I stopped doing the chop because it was messier, and because I was having difficulty getting the head to come off with just one neat blow. I guess I lack the arm strength, and also found myself hesitating right at the moment when I needed to be decisive. I wasn't doing the birds any favor by chopping them gently, but it was difficult to overcome my instinctual feeling to "be nice to the chickens".
It was a bit unnerving at first to do the throat-cutting, to be so close-up & personal to The Deed. But when I saw how quickly the birds went limp (before the reflexive flapping) it didn't feel so bad. I get them very relaxed, and hypnotized to the point of slumber, it's all a very calm & quiet event.