I've dealt with a few of these, so first I'll start with addressing your questions/ comments in your post.
Hi! I'm riding a horse who curls ridiculously far behind the vertical. It's to the point where he could fully have his neck extended with the length of the rein, and will put his nose around six inches away from his chest. I've been riding on a rein with no contact at all, and just relying on my body, but his neck remains curled, and his back down.
First, when you say "riding with no contact", what does that mean? Long rein? or Giving away contact? It sounds like you are giving away contact when your horse 'gives'. Is that correct? So, it sounds as if you are working on a pressure and release principle in order to attain a frame? By bringing reins back or touching the reins, your horse gives into pressure. The reason that this does not work is because the horse is evading true contact by giving into pressure. You want your horse to do the opposite: move into the bit and this comes from engaging the hind end and abdominal of the horse first.
Recently, I've been pushing with my seat and leg (more than I was) when he curls, and he'll bring his neck a bit straighter, but will then start throwing his head (still without contact or pressure).
It's good that you are using seat and leg! You do need seat and leg to encourage your horse to use his hind end and come forward; however, be careful he is not losing balance (becoming too fast) as he will also plummet onto the forehand making it harder to use himself properly. As for the head tossing, I'd think that this is a combination of not having built the proper muscles to hold a correct framer, and also not knowing what to do with actual contact. One horse I had worked with was a head tosser. His head tossing went away as he gained more muscle and confidence. The only time it has reappeared (as far as I know) is when green riders with less steady hands have hopped on him.
He has been checked by the vet and chiropractor repeatedly and does not appear to be in any pain in any part of his body or mouth. He is currently in a loose ring snaffle with a roller mouth. I have brought up trying him in a straight rubber mouth, or a three piece copper/ iron or coated mouth, or a different roller piece, possibly even a hackamore, but the owners refuse (I'm exercise riding him so I don't have any official say).
That's a tough one. (1) because if there are others riding him and NOT following through with the same consistency, then his old habit may be continuously reinforced. If you do get somewhere with this horse, he can easily go back to curling shortly after. Then, you may get somewhere with him in a few rides and find out that the next ride he has gone back 3 steps. I still encourage you to learn from this experience; however, just keep in mind that there are going to be several limitations. (2) There could still be undiagnosed pain or poor saddle fit without your knowledge.
Any suggestions? It's not like he doesn't listen to my seat or leg, but curling like that isn't good for him, and there's no way he could show like that.
First, I'll say that you will have to go backwards before you go forwards. Meaning, do not worry about framing him up right now. Your main objective will be to have him take the bit or put weight back into the bit, as he is doing the complete opposite right now. I'll post a video on what to do with your hands, as I think the video shows it much better than I can describe it.
- I will mention that I'm not crazy about "wiggling your inside hand to soften the horse" and feel that could be counter productive on your horse particularly. If your horse has tension with the bit, then that should be addressed long-term. The wiggling, at least to me, is a quick fix method. Although, you can use the inside rein to help place the horse in the correct flexion without wiggling-
Every time he goes behind the bit, you want to pick him up again.
Ideally, what you'd like to encourage the horse, once you've picked him up from curling his head, to stretch forward to the bit and down. Keep your contact with his mouth and slowly allow him to move his head forward and out, as you close your leg. If he does not move forward, then do not give away contact. Keep it and try again later. If you do normally ride with a long rein, then you may need to shorten to a medium length. I've never done so with a long rein or western style contact, although I would assume it would be a similar process. Maybe someone else here has suggestions for that.
Also, keep using your leg and seat to ask for him to come forward, but only to an extent to which he is balance. When a horse begins curling, seldom will just sending him forward suffice, as this is normally an issue from avoiding bit pressure and not only falling behind. If he does get to fast, then half halt with seat or ask him to walk. At this stage, try not to use rein in half halting if possible.
Lastly, this will take time and often lots of time to correct. If curling has been a regular occurrence, then the muscles you don't want to build up (such as under the neck) have built and the muscle you need to hold a correct frame are weak. For a while, at least, this horse will not be able to hold a correct frame for long, so reward and encourage all the small attempts well.