Recently we brought only our foil kites with us on a kitesurfing trip to the British Virgin Islands. With zero previous experience launching, switching and landing foil kites from a catamaran, this is what we learned. Enjoy!
Great video, showing genuine experience is good. With a foil kite the key points are to have it laying flat, no folds etc, LE away and TE towards you, like for a hot launch. You want to have it inflated a bit, enough that the air intakes will work. You want the bridles all sorted before you let go. It is important your bar is wrapped with no tangles and evenly. You can let out the kite with no tension or some. The great thing about foil kites is they will stay on the water well until you inflate them or give good line tension. The other thing is you can flag them with any line and very easily which you see you can't with an LEI. I personally would have hop in the water before I launched the kite, to avoid any issues with the boat. Having a bar setup with oversheeting is key to better kite control. You can fly a kite anywhere in the window you just need more rear line to make it fly deep.
So watching the video to the end I see you got some of those points in the end. To swap users you could do it in the water or you can land the kite in the water either at the edge or downwind, just do it onto the TE. One person holds the rear leaders in to hold it down while the other swaps the chicken loop/connection.
An alternative to landing on the water, though much less safe and easy, is you could land from the water onto the boat. You are likely to just end up wrapping it on the boat if you are not careful. The idea is to have someone catch and flag the kite off the back of the boat. A dinghy is much easier for this. Your lander can retrieve the kite with out it getting wet, but again not easy.