Collection does not depend on how much their head is curled, that would just be called "framing up".
I think what you are wanting is to have your horse "on the bit"(for correct terminology). When your horse's head is curled, your horse is not on the bit but rather is using that as an invasion of using himself.
Once your horse starts to use himself, on the bit comes naturally, without the curling. In order to achieve this I will agree with jazzyrider and start longing him (side reins, longe line, longe whip). I recommend the side reins that has the donut attached to them, because when the horse gives into the contact, the donut gives and it helps them learn better. At first put the side reins on looser and gradually tighten them to where his nose is vertical to the ground or slightly above the vertical. Use your longe line as your rein and the whip as your leg. When you longe your horse work on your horse doing nice forward and clear transitions(walk-trot, trot-canter, canter-trot, trot-walk).
After you longe, you can ride him and keep the side reins on. When you ride him work on keeping consistant and steady contact to the bit. Work on the circle with transitions and bending lines.
I hope that all helped..
It all takes time and consistancy. Just be patient and it works out. For the most part you seem to do a good job, just work on keeping a nice consistant contact.