I apologize if this gets lengthy; I'm the queen of overly long answers hehe!
I work with a lot of OTTBs, and several of them come off the track with tendencies like that - some cock their heads, some open their mouths, some stick out their tongues, or cross their jaw, etc. What it comes down to is a lack of understanding of the bit.
When they're on the track, the bit acts as little more than a steering aid and a balancing aid. The jockey uses a bridge to balance himself against the neck, and give the horse a stable point so that he won't get too low and fall over himself - basically, the horse can lean on the pressure to keep his balance. It's not used at all like in the English disciplines, in which a rounder, softer carriage is desired. But you also have to look at a racehorse's hind end - because the hind end is the most important part of your headset. A horse can't be "underneath himself" at a gallop in the way that he can at the other three gaits - it's an elongated gait, and the hind end is out behind him, pushing and propelling him forward. It comes under during part of the stride, and the horse compacts. It goes out behind, and the horse's frame lengthens.
Here's the compact, underneath-itself frame:
Versus the long, strung out part of the stride:
See how the horse's body length changes? It's the same principle we use in dressage/hunt-seat/whatever. You want the horse to be compacted.
So, to answer your question (finally, right!?). Your horse is avoiding the bit because he's confused about what you're using it for. He has been trained to lean on it and pull - you won't allow that, so he tilts his head, which is harder for you to get him to stop doing. I think, too, that he may not understand your leg - because, as you can guess, jockeys aren't doing much in the way of leg aids with their knees under their chins!
This is why retraining an OTTB is a gradual process - albeit a rewarding one. The first thing you need to do - and this MUST be tackled first - is teach him, patiently, what the leg means. Walk-work is your friend. He must understand go, first of all. Get him in front of your leg, with a very, very light contact - almost none - and get him trotting out, big. It'll feel fast; let it.
Then he needs to be super aware of moving off the leg. Slowly teach him to yield, left and right, to your legs. Teach him a baby leg-yield at the walk (with a loose rein - it won't be a true leg yield, but it's very effective). Teach him to stop when you sink deep into the saddle and put on a little leg pressure.
This may take days, it may take weeks. Let him tell you how much time he needs - that patience will reward you later when you have a fantastically well-based horse!
Once he "gets" the leg, you can introduce the concept of pressure up front. I like starting OTTBs in a single-joint, medium Dee, and then moving to a double-jointed loose-ring when they understand the bit. A Dee is commonly used in racing, and the familiarity can help ease them into a situation. Work on 'setting' the outside rein, lightly, and using that inside leg that he by now respects so well to puuuush him gently into it. He'll be confused, it's okay. Baby steps are key. Work on this in both directions, giiiiiving and praising if he yields even a little. Don't pull back at all. And remember, pressure should never be continuous. The key to training is not negative reinforcement, it is little gives and releases of external pressure when he's done well. You can work on your baby leg yields with a little contact now, but leg should still be number one. When he is happy with the outside rein, you can play with the inside one, too. By play with, I mean treat it like a sponge. Don't rely on it like soooo many people do. If you're doing it right, you can go through an entire ride with a totally loose inside rein, switching when you change directions. It should only be used as a mild reinforcer, to get that leeetle bit extra bend, and then a GIVE when you get even a bit of yielding. I could preach all day about the power of the give!
All this will eventually lead to a total understanding of what you want, and how to react. It's like teaching a German foreign exchange student English - you wouldn't hand him War and Peace as soon as he steps off the plane, would you?! Your horse needs some 'See Spot Run' right now ;)
But don't worry - TBs are VERY smart, and very quick learners. If you're patient, nailing the basics won't take long. Good luck! :) And if you need me to explain anything, let me know. ;)