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

bit of older footage thrown in the mix when Mitu did a lot of strapped riding in the cross off wind. Hard to see but he is strapped in the 1:51 fall to recovery move. Its strapped until he picks up the board leaning against the tree at 2:18. 2:50 is what i was talking about with what you have to do if you "send the kite" looks silly, is fun to try...for a while

Thanks for great take on it richierich. I'll try and man up and give the kite loop a go. Strapless aerials seem to be a slow learning curve.