I agree with most of this...sometimes though there is that 1 in 58349857348 chance that it is something physical. My mare acted the same way as OP's horse. The chiropractor came out and adjusted her, she was still the same. He came out again, noticed her ribs were out and adjusted her and she hasn't been cinchy since.
It was completely by chance that we figured it out this way.
OP, has he always been like this, or is it worse in the winter months?
Could you take a close up picture of the girth and billets when he is cinched up next time?
If it isn't physical- Foxhunter is absolutely right, it can take a very long time to correct the behavior.
My gelding has always been horribly girthy. He knows he had better not bite at me, so he bites the air/at the saddle on whatever side I am not on.
I always figured he was being a huge jerk since there was "nothing medically wrong," so I'd bop him one in the nose if he showed me any part of his face during the girthing-up process.
Then it turned out that he has PSSM2 and girthiness is a super common symptom.
Now that the PSSM is being treated, he's barely girthy at all - he may pin his ears out of habit, but there's no biting at anything.
Not saying that PSSM is at all at fault in the OP's situation, but I just want to point out that a horse can be deemed 100% healthy by numerous highly competent vets and still have something medically wrong.
Of course, that being said, PSSM or not, my gelding knows that he's gonna get walloped if he tries to bite me. Pain is no excuse for a dangerous behavior like biting. He can demonstrate his discomfort in other ways [like biting his off-side] and I'll respect that, but he had better not try biting me
For my gelding, since I know that he assesses the situation before biting, I know that he's gonna turn his head towards me for a few seconds before actually doing anything.
With him, when I see him thinking about putting his teeth on me, I warn him by saying "ah-ah-ah." Usually, because he knows that he's been caught, he immediately stops thinking about biting me. If he escalates by pinning his ears or actually nipping, I'll smack him hard on the neck and immediately return to whatever I was doing.
I rarely, like once every year, have to resort to actually hitting him. 99% of the time, "ah-ah-ah" is enough of a warning.