I watched the first video (at work.. NO sound on) and your read of the horse is not something everyone can do. When he turned and put his but toward you I saw you not allow him to go in the new direction but if he turned with his head toward you, you immediately released the pressure... sideways stance, no eye contact, gave him space.
Lots of very nice subtle work. I happen to be training dogs with someone who operates very similar.. the instant your dog is on the field with him, he is communicating with the dog and it is subtle.. most ppl miss it.. but the dog does not.
I used a lunge whip when I did this (had knee surgery in 1984.. and am getting a new knee next week). I only used the whip to be a little more precise and because with a bum knee I could not always get where I needed to when I needed to and it was like having a longer arm.
Been thinking of moving to AL when I retire (northern AL). Hoping to have about 20-30 acres, good outbuildings.. maybe do a little of this sort of work if I still can (6 years away). Watching this gives me something to think on.