above your head is undoubtedly the worst/least safe place you can put your kite. don't be stupid.
(although the design characteristics question is interesting i guess.)
you gotta think outside the box a little. Arcs have been doing it for years and years. To be safe you also need it to remain stable as all fuck once its up there and for it to have virtually no power. Arcs do all of that pretty well despite the story above. I parked one on the end of a dock and left it up there, had lunch, then grabbed it and hit the water again. In winter you can tie em off on an ice screw and have a beer and it will wait for you like a horse at a post. Not safe or smart or whatever, but in consistent wind a fully developed feature of other kite designs. On even a remotely appropriate size arc, they just sit up there and wait. I've more than a couple years on both types and tho I no longer fly arcs, the feature could have huge merit for wave purists as your kite is a thousand times less likely to ever get washed. That kite could be your lifeline in the event you really get tumbled and if it stays flying Id say your less likely to see tangles.
Ive had 5 line C kites that when you go to safety would fly super stable from the 5th. Super handy on sketchy exits, and any kind of mud/weeds/rocks etc.
An auto zenith 4 line kite that will safety straight up is really what you will eventually get when designers try for ever more stable wave kites. What could be more stable than a kite that corrects to the middle? I eventually really didn't like having a kite pull up while riding. It requires you fly it from the bottom hand, instead of LEI's than tend down, you have always been able to fly well with a hand on the top side of the bar. If the trait were done right there would be little to no drift while riding and actively flying the kite, but it would safety like my old 5 liners.