I started a Morgan gelding who appears, from the exterior, to be an extremely calm horse (and he is), but he’s also mouthy/pushy and shows his anxiety in this way. Anxiety doesn’t always manifest in fear responses or the kinds of things we typically think of when we think of nervous horses. And yes, he also had a very similar routine - he’d go to put his mouth on you but then retreat quickly as he knew what was coming in response.
Bottom line with him, and the same with your horse - if you’re responding to something he’s already done, you’re late. You need to catch him in the act of thinking about it and either redirect his attention to what you DO want him to be doing or, if he goes to try it, you let him create the correction. I think you mentioned earlier in the thread letting him meet your elbow, which is an excellent way to deter a horse from getting mouthy because HE creates the pressure he ran into, not you. When you have to come at a horse, you’re late - if you’re already there when he goes to do something and he makes the error of running into your elbow, or a foot-long chunk of a broom handle (which is what I used for said Morgan gelding) he thinks he did it to himself. He’s a lot more likely to heed that lesson.
Without seeing your farrier work versus you work, it’s impossible to know for sure what the difference is but my guess is the energy and timing of your farrier is the main component. Consistent handling in this way will surely help him become more relaxed, but like the Morgan gelding, he will probably need this way of handling for his entire life. The smart ones usually do.