I'd thought I'd through some thoughts into here, because I've ridden my fair share of fresh OTTBs. ...And racehorses. Ugh!
I can see that your hands are attempting a contact--light but there, where the reins are still somewhat taunt but the horse isn't cranked behind the vertical. However-- with the short time he's been off the track and actually in work, I do not think /he/ is ready for the amount of contact you are trying to give.
Relaxation always comes first. For a horse to tuck his nose behind the vertical, he has to be tense in his jaw. If he is tense in his jaw, good chances are he is tense somewhere else. In order for a horse to push his body and carry it correctly, the push has to move through an elastic back, up and out of the poll. When his head is behind the vertical, you put a kink in the 'flow'.
If he is rushing, he is either nervous or unbalanced. One or the other, not something else. If he typically rushes at the canter, it is not always a 'oh he was a race horse' deal--most racehorses aren't taught to carry themselves they're just taught to run. I would leave canter work out of his workouts for a while. Above all other horses, OTTBs really need a lot of correct trot work until they can canter. The canter is the test of your walk and trot--if they are not solid, the canter won't be either.
By creating the contact you are helping him lean on your hands for support. At this moment he is not ready, mentally or physically, for contact. He may /want/ it because that's how race horses are trained, but he really just wants the crutch part of it, where he can set against it, no matter how light.
I would personally forget about his head altogether and get him to move relaxed in every gait--you can expect him to reach for the bit until he can be relaxed. Long and low work is an absolute must--he has to start now, to free up his back and allow him to learn to relax his muscles. Think about race horse training... they are taught to be tense and taunt all the time, so you're going to have to overcome that before you can worry about his head.
Of course, you don't let him start gaze. If he roots his nose out, you just ask for soft, lateral bends in the neck until he relaxes. When he does, the head and neck will come down. You want to work him low and stretching before you ever start to bring his head up--but you don't ever ask for the nose to come under the poll. That's his job--not yours. The reins have a lot of jobs, and have to tell him a lot of things--when you start telling him that a slight pull means 'put your head here', then the squeeze of your fingers for a half halt doesn't really mean anything but, 'keep your head here'.
By working him in a lower frame, you will teach him to stretch his neck forward and out. Eventually it will be forward and into the contact, and the push of your legs and seat will not mean, 'run away', it will begin to mean, 'push your energy up to my hands, please!' And when you find that the back end is connected to your hands... THAT is when you take up your contact. Mainly because you won't have to--he will be doing it for you. A higher neck is never a result of your hands--it is always from proper training.
Let him move out at the canter when you get there, perhaps more then you think is correct. No rushing, but let it have a lot of impulsion. TBs don't understand 'canter slower, please'. That just means, 'lean on the hands and canter on the forehand.' Only begin with a circle or two of the canter. The moment he begins to rush away, or get crappy, just ask him to go back to a trot. Horses were born with knowing how to canter with us on their back.
With that being said, I don't think he's the most tense, crappiest horse I've ever seen.
I just think you have the potential to be riding your horse better then the general population's method of 'hold the head, push with the legs'. He's a pretty horse and I think you've got something nice on your hands as long as you are careful with him.
Now, for you.
I'm sure a lot of people will slam you for your heels, but I don't like the traditional 'cram your heel down' method. I would like to see JUST a little more bend in your ankle, which will be achieved when you pull your thigh back (not your calf!) and push down. That should get your heel back where it belongs, which it often creeps too far forward.
Now I could be incorrect, but it also looks like you post out of your stirrups, and not from the leg/thigh. When you're in your trot photos, that's where it looks like the weight is on your toes--because you're posting, I would assume?
Don't think about trying to pull your shoulders back to straighten your back. Think about puffing out the bottom of your sternum. Ride like 'a capital D', with the straight part being your back of course.
Helps me a lot!
I hope this helps! I tried to be as constructive as possible.