Yep MelissaAnn, TB are interesting creatures and you do sometimes need to change how you would train another horse, to fit them. Horses are all very different, we can't train them all in the same manner. And though I would usually recommend trying to perfect one thing before moving onto the next, it sounds like the things you're trying to perfect are the smaller, 'nitty gritty' details.
Even if you're not into dressage, it's worth looking up the German Training Scale. This will show you the order in which training should progress to give a horse the best chance of development and success in any under saddle work.
The base of this pyramid of training, is occupied by 'rhythm', followed by 'relaxation'. Forget 'on the bit' and doing schooling figures, trying to make them perfect shapes etc.
Until you have rhythm, you're not going to have much luck with anything else. To get rhythm on an ottb, sometimes you do need to be a little unorthadox in your riding, as opposed to riding say a warmblood. But the key is forward. And the mistake people make in riding ottb's, is that they believe that the horse IS forward, because it runs off all the time.
This does not constitute forward - forward is when the horse reacts and responds positively to a rider's driving aids, by moving the hind legs further under the horse's centre of gravity, and pushing off the ground with increased energy - controllable energy.
So may I suggest this. (and if he is feeling fresh and toey, though usual warmup is to walk for 15 minutes, go straight to canter, get off his back and let him canter it off for 5 minutes. Go large around the arena, put in 20m circles, increase and decrease the size of the canter, until you feel his brain is coming back between his ears and he's starting to focus on you).
Start at halt. Will he move immediately off your leg with a very light tough of your calf? If not, ask him nicely with your calf, then back up that aid with a flick of a dressage whip on his hind quarters, or a bit of a kick.Grab a chunk of mane so you don't pull on his mouth if he jumps forward - if he does leap forward and take off, that is ok, let him because he moved forward from your aid. Just give your reins, let him for for a few meters and bring him back in on a circle to slow him down. Repeat a few times, until he doesn't jump and run so far. Don't expect perfection in the first session, if you keep working on the same thing for 40minutes straight, he'll think of evasion tactics and you've then wasted your time.
Same goes for walk - trot, trot - canter. Expect him to give you a forward reaction every time you put your leg on. Without a go button, you cannot have a stop button.
Now for for stop button, there are various methods you could try, I'll give you one that works best for me.
Start at walk, completely relax your body, let your legs hang and go floppy. Now 'breathe' your weight down into your seat bones, and block the walk motion with your hips. Your horse will feel this resistance to it's movement, and will usually slow down. As soon as it slows down, even if not a complete stop, that is a positive reaction, so reward it by allowing yourself to move with the walk again. Go for a few strides, then repeat the aid. When you are consistently getting an immediate slowing reaction, then you know you've done the right thing and your seat has influence over the horse.
For the full stop, repeat the aid, but you may need to ask just a little with the rein. So first use your seat aid, when the horse slows, keep the aid on, and ask with the rein, using a little closure of your first to block the forward motion. Keep the aid on, until you get a stop, then release immediately.
I have usually taught this over a number of lessons, again, because you don't want the horse getting bored. You can throw them in all over the place in your ride, there's no need to work soley on the stop button. But the goal is to get a slowing reaction purely from your seat.
The same thing at trot, relax, deepen your seat and hold your core until the horse feels the resistance and slows, then add a little rein if need be to get the transition back to walk.
Now, I may get my head bitten off for this, BUT, no, it will not ruin a horse's mouth. If your horse is extremely persistent on running through your hands and taking off, sometimes it pays to 'take their back teeth out'. Lift your hands up and towards his poll (not back towards your body) and give him a 'Hey you, bloomin' listen to me ok! I said STOP and I mean it!!'. The second he comes back to you, completely release the pressure and ride on like nothing happened. You're not going to ruin his mouth with the occasional check on the rein like that, as much as people may tell you that. I've used it on a number of difficult horses with zero stop button training, and you know what? I've never had someone tell me that a horse's mouth has been bad when they've ridden my horses. They've all ended up being very willing to work up into a contact, and just a squeeze of my finger can get the desired result in flexion and submission if need be.
Its the people that constantly haul on their horse's face that create a hard mouth.
Ok, so you've got 'go' and 'stop' buttons installed. NOW you can start working on rhythm. Rhythm is the speed and tempo at which the horse will relax its body, mind and swing its back. The good tempo for walk is around 95 beats per minute, 150 bpm for trot, and 98bpm for canter. Give or take a little on each to allow for individual horses, but this is roughly what you need to be aiming for.
TEMPO = Speed
RHYTHM = regularity of that speed
Find the appropriate tempo for your horse, and work to maintain that tempo with your body. The tempo should not change for extended or collected work.
It may help to compile some songs that fit the horse's walk, trot and canter tempo, and ride to those songs, to help you maintain the tempo and rhythm. Sometimes it is easy to allow the horse to get a little away from us without noticing, and soon we're back out of control going a million miles an hour down the long side! So you really need to be aware of your tempo. Thoroughbreds generally aren't horses with a natural rhythm, so you as a rider needs to dictate this.
When the horse finds its rhythm, I guarantee, it will start to relax its body, and be far more willing to comply with you. THEN you can start moving on to developing the more 'fun stuff' :)
Hope that helps you!