Well, here's a different way.
I wind one of the pairs, starting from the staked handles, ending up at the kite. At that point I unhook both pairs from the kite, and pack up the kite.
Then I start winding the second pair on the same winder, ending up at the stake, unhook the second pair from it's handle and I'm ready to walk away.
Next time out, I hook the outer pair of lines to the first handle, hook it around the stake with the bottom, trailing edge line out for slack. If the wind isn't too strong, I can set the kite up leading edge down, hook up the second pair of lines and unwind back to the stake to hook up the second handle. In higher winds I'll weight the kite down with sand and walk back to the kite to set it up after staking out the lines.
I'm sure this isn't the fastest way, but since each pair is wound separately, the pairs won't tangle.
Doug L.