Brian,
I know the frustration of having a great wind blowing, limited time and a birds nest of dyneema. So here is what I do which works 95%+ of the time:
1) Be methodical ... more haste less speed & therefore less flying time next time out!
For the kite I use a strop with a loop at either end. I larks head the upper and lower bridle lines together. First one side then the other. This means that they don't get too tangled or wound round each other. I roll the kite up and put it away. When unfolding the kite I grab the strop and let the wind take the kite. At this point it is usually easy to see how to get the bridle lines straightened out.
I always unattach the kite from the lines as I use the same lines for more than one kite. If you only have one kite this may not be an option you like as leaving the lines attached may be more effective. The strop method is the same principle as leaving the lines attached however.
For my lines ... I use Tradewinds figure 8 winders for all but my longest and heaviest quad line sets...:
1) Put the stake in 2) lay the handles over the stake 3) walk out the lines 4) pull on the left and right lines separately (This removes mirror twists ie: one clockwise cancels one anti-clockwise) at this point the line set should look pretty untangled. 5) return to the stake and feed the brake loops over the stake 6) pick up the kite and walk down the line set holding / untangling the left & right pairs as you go. 7) Attach kite ... Waaaaaaaaaa! have a blast 8) Land kite and attach brake loops to park 9) disconnect kite one side at a time and attach bridle lines to the strop mentioned above 10) pack kite away 11) attach the lower lines to the upper lines using a larks head making sure left goes to left and right to right! 12) walk back to the stake and remove the handels from the stake laying them out flat 13) walk back to the end with the winder and hook the upper line loops over the winder notch. 14) wind progressively from the front to the back of the figure eight winder. When you get to the back jump straight from the back to the front in one go then proceed slowly to the back again (This means that it unwinds cleanly ... I could explain but think about it yourself!)
Hey presto! ... well I did say you need to be methodical. My problems usually occur when I have difficulty putting the kite down after flying in winds that pick up. At this point I can't be too fussy about getting the damn things packed!!
Cheers ian