I don't know if this will help since it's like the opposite of what you are doing, but when I was like 9, my trainer would have us "run" horses that couldn't be caught in open fields. Looking back, I'm not sure if it is ethical but I was young so please don't bash me for it people! Lol I've done it a few times over the past few years and it has always worked for me. Though my horses weren't scared of the halter, they just didn't wanna get caught haha
Anywayys what she had us do was walk up to them like we normally would to halter them. If they would run off, we would run after them for about 10 steps and smooch and flail our arms. Eventually they would stop at some far end of the pasture and we would calmly walk over to them, keeping our eyes down and bodies slouched (no threatening). If they would take off, we would repeat the above steps as many times as it took. Usually after about twice though they would realize it was easier to just get caught and we would have the haltered :)
Again, I don't know if this is quite suited for you since your horse seems to be more timid and afraid of you/the halter at some points instead of just ornery about it... You seem to be making progress with what you are doing though!