Here are my tips for wave barrels with a kite.
Before starting your ride give your bar one spin, this way your lines will be twisted close to where they will be going through the lip. This will avoid your kite being pulled down when your lines go through the lip (the bottom line always gets more pull and ends up by crashing the kite behind the wave).
If you get eaten, even badly eaten, pull the kite into a loop (or several). The wipeout won't even be one then, as the kite will pull you straight out of harms way.
This worked great for me a the last KSP where I had one of my fatest wipeouts in the first day local elimination heat. I thought I was dead for about one second and the kite 'extracted' me from the maelstrom.
Last thing you want in the waves is a kite down.