if you 'send it back' you won't be able to keep the board on your feet. You can't press it into the wind cause you've lost the wind by moving the kite past 12. If you grab the board on the way up thats fine but you can't steer the kite back forward unless you do a Mitu and but the board between your legs to change hands. Other options is to catch it with your front hand and kiteloop it with back hand- make sure you have a strong board to land it. Watch this Mitu video or look up Keahi or Airton who are the masters of what is possible freestyle strapless.
Personally i would work on your 'chop hop' and bring the kite up a bit as you take off but keep kite same direction as you are going. hope this helps