OK, haven't read replies yet, thought I'd just comment on what I feel from your words...
Background is, he is 19 years old, an OTTB, we only do dressage (Training/First level). He is ridden probably 4 days a week solid, sometimes more, sometimes less.
Perhaps you're only doing 'easy', low level stuff with him, but dressage can be incredibly hard on a horse, esp if they're not very fit & sound to begin with. A 19yo OT horse, I'd be inclined to think it might be too much for. Not sure what you mean by '4 days solid' - do you ride for many hours a day or some such? How does he live the rest of the time?
'Head bobbing' does tend to indicate significant discomfort, even if they're not obviously 'very' lame to us. Horses are incredibly stoic creatures generally. I'd think of head bobbing as more than 1/10 lame. It is often also an indication of a hind foot/leg/hip problem too - eg. Bobbing on the left fore is often because of right hind probs.
You say he's got 'typical TB feet'. Without pictures, can only guess, but I'm imagining he's got 'splatted' flat, thin soles, flared walls & underrun heels. This is something that will be very unhelpful(whether it's actually a cause or not of this thing), and getting his feet healthy & able to function better, including providing support as necessary, is something I'd be treating as a priority.
I also wonder, if he's lame & out of action, why are you keeping him shod? I suspect you were thinking it would be a short term prob & you'd be riding again? I wonder, why does he need shoes at all, if you only ride him in an arena? Esp why you need to put easyboots on his 2 unshod feet, when he's not being worked? Are his feet that terrible? That it sounds like he's lost 3 shoes in as many weeks - is losing shoes common for him? - sounds like there is a real problem there, be it just with the farriery or otherwise. I'd be inclined to keep shoes off him for a while, until he can develop some strength to his weak feet. Why have 'his feet gotten bad'? Is this recent, that they've got a lot worse? Pics??(see link below)
So... he's got terrible feet, has ripped shoes off repeatedly, is 19yo & had a lifetime of jumping & racing, now dressage. Is lame on left hand turns... Of course it could be a number of different things, but I'd start with rads &/or MRI of his feet, and get him well checked out by a vet chiro or such, and get a good farrier. As mentioned, I'd be inclined to keep him bare & boot him when necessary for protection/support, but if he's going to remain shod, he needs to be well shod with attention to balance, and adequate support under his feet - not just a rim shoe.