All good points, I would add the following tips regarding the wing handling.
1) when entering the gybe keep the front head straight above your head (just a slight angle in front of you).
2) let go of the back hand and do not move the front end while you start going downwind, the wing will start turning on its own
3) when going downwind, without moving your front hand and arm, place your former back hand on top of your front hand, then let go the former front hand. The point here is to switch front hand without having the wing moving in front or behind you.
4) after that, you keep turning and place the former front hand on the back handle. If you did correctly point 3, you will find very easy to get to the back handle without having to move the wing. Always remember that it's the back handle that reaches your hand, not the other way around. By that I mean that if your back handle has moved too far to reach, then you need to move the wing with your front hand in order to bring the handle closer to you. What you don't want to do is leaning forward with your whole body to reach for the back handle, this will put you off balance and you will fall.
It's easier to show than to describe it, but hopefully it makes sense.
I strongly encourage practicing this on the beach by walking downwind, as if constantly gybing, so that wing handling becomes natural and the focus can be on the board while trying it on the water.
I often see people hang onto the wing for too long with both hands when already going downwind. The trick is to let go early enough, and continue turning just the foil, instead of letting the wing pull you through the turn. Just illustrating your good points with a clip where I film the progress of a student who was already quite comfortably nailing the jibes where he stops completely, but at that time he hadn't made one with fully foiling. I deliberately make all the movements in my jibes very slowly, for teaching purposes, and I would add one key moment that I think is helpful. Keep both hands extended, in front of you - that helps to keep the weight distribution the same throughout the turn.
Nice video! I would add that the bigger the wing is the higher you will need to keep it so that it won't touch the water.
As you mention, you do not need the wing power to gybe, get some speed before starting the turn.