I sail Formula 18s. My experience with gybing a kite is that it is mostly pretty tame in up to about 22 knots of breeze. That is because you are doing windspeed or better with the chute up.

While sailing downwind the main is almost center travelled and sheeted pretty tight to get the telltales to fly. Most of the time the windward hull is in the air. Give your crew lots of warning before you gybe. I start my warnings about 30 to 60 seconds before a gybe, that way she can prepare coming in off the wire. During the gybe I loose the main traveller out about 1/2 way. She keeps the spinnaker sheet, she was holding, fairly tight while she pulls on the other. The idea is to sneak the sail around the forestay. On the opposite gybe I travel in while she sheets in and hopefully we have completed the gybe enough to be flying the new hull immediately. While turning down I try to do so smoothly keeping the speed up. I am trying to keep the boat going faster than the wind. I do not even feel the main hit the other side. I just hear the pop of the battens, and then feel lift off. A great gybe is a thing to behold.

Later,
Dan