I have a Hilleberg tarp rather than a DD.
I keep the cords separate, guy lines have lightweight mini carabiners on them, I find that leaving guy lines attached to the tarp often results in them flying loose and tangling when it is windy.
The tarp is simply stuffed into a rubble bag that can be compressed to fit every possible bit of space in my pack. If I'm carrying tent pegs, they are held together with big elastic band and the pointy bits placed in a cut down half litre cola bottle, which is then shoved into the tarp bag.
All the cords are kept in their own small stuff sack.
I find I can get a shelter up quite quickly.
I once had a Hennessy Hammock with snake-skins and if I was on a cross country speed hike or similar I'd probably choose that again.