Hmm - odd, I would do the exact opposite
When and after turning around on the wave (the chicken jibe), I would keep the kite quite low !
This way it has line tension, and you can always MOVE the kite, if you need more tension, or can see slack lines getting closer.
If you fly the kite high, you have put yourself in a blind alley with no options but to pray
As then you got no line tension, so you will most likely force the kite to hindenburg yourself, when riding towards it.
And you can not change kite direction fast, or not at all, with slack lines
So when you've turned around, keep the kite quite low and with some speed, then it will sit stable even if you go a bit towards it
Bottom line is, its all about timing and experience - I dont think there is anything wrong with the kite at all, just lack of practice.
When you have the kite lower, EVERYTHING is possible, and you will soon learn how to move the kite around without thinking about it - and in superlight wind you'll just loop the kite when appropriate - on your backbone.
You can also try to head a bit more upwind, when going toeside away from the wave - as this will also solve the problem easily.
So could be a matter of practicing this too ?
Finally, like others wrote - it could be your timing, that you send the kite around too early, which is really bad of course.
Often the opposite happens - that you jibe on/before a huge wave, and the speed you get when going "down", will give you shitloads of power in the lines because of the apparent wind, so you have to go a bit more downwind to take the pressure away...
What wind direction are we talking about, almost sideshore or 45 degree ?
And when you write you "dont really try to ride waves on it" - what do you mean - are you on a TT or on a waveboard ?