Can you see how much more forward your horse is? He is not sucking back, nor is he being pushed or rushed. He has found his rythm becuase you are able to be with him, and not impede him , at all. This is wonderful with a capital WWWWW.
The first videos were painful to watch, the last two say, this pair are comfortable and I'd love to go riding with them! We'd have a blast.
You have improved your hand position, but it is still not being utilized to bring as much unity as is possible.
#1 at the very least, rotate your hands so you are not palms down. Think of bringing your hands and palms together, and almost as if you are holding a gift between them, and think of just "offering " them forward to your horse . I don't mean that they actually go way out over his neck. But that the energy that comes up through your body, from the saddle, you kind of hold in your hand, in stillness, softness, but NOT a weak open hand, and say, "here you are" and roll your palms upward a bit. To compensate for the bad habit of keeping them down, think of offering them upward and together.
In time, you can work on making the contact be flexible from completely loose to having enough contact for the hrose to find it and respond to it. For now, your horse seems pretty happy on the contact you are offering him now, and for trail riding, you go loose unless you need to pick up the rein for a stop, turn, or some other change.
Well done, all around! And, your horse is lovely.
I do occasionally see a tiny hitch in his gait, maybe front right? Not sure. It seems minor, so not sure if it's just rough ground.