Do you ride English or Western? My Appendix will drop his head when he is out of shape and is ridden collected for to long. He was seriously out of shape after winter and my trainer was riding him and I kept telling her to let him stretch his neck and finally he just dropped his head to the ground. Lots of breaks till he is back in shape. The other thing I can think of is sometimes they do that to get away from a bit that is hurting their mouth?
From everything I have read about Chinga, it sounds like to me that it is a way he has learned to evade the bit. I would work him constantly using only 1 rein at a time. With his issues, it sounds like most of them stem from using both reins. I can't remember but I think you ruled out pain for all of his other problems, right? If it's not pain, then it is habit. I wouldn't concern myself with the canter until you got the bucking issues under control. Then, when you start cantering, start with medium sized circles. Keep his neck bent just a hair to the inside and if he starts to drop his head, pick up the inside rein and outside leg to urge him to keep his speed and level out. I won't guarantee that this will work but it is something to try.
Dakota does that because he was trained in western before he was trained in english, but he also does it to be naughty sometimes. What I do is lift one rein up and give a big kick. That usually does the trick.