What about wrapping them around some other gear or a light weight object dedicated to the purpose, like one of those plastic phone cards or something?
Also do you ever leave the lines partially rolled up if you're pitching the tarp edges close to the ground?
Here's another couple of techniques to ponder that can reduce tangles.
Fold the guy line in half, then in half again. Repeat until the bundle is a manageable size (4 or 5 folds). Tie the entire bundle in a half hitch.
-- or --
Fold the tarp in half. Tuck the loose guy lines into the fold. Continue packing up your tarp.
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