My method is similar to Pan's.
I also do the lines the same way. But before I untie an end from the tree, I shake as much wetness off as I can, then I flip the tarp over so it is wet-side to wet- side )unless it si currently raining). Then, similar to pan, I untie one side. But instead of bringing it to the other end, I fold it back and forth at about 1 foot intervals. When I get to the other tree, I pull the slippery tautline hitch and then roll down from the ridge to the loose end. This allows residual moisture to be squeezed out. As I get close to the end, I tuck the the lines in, and use the tree lines to tie up the bundle. This gets put into the bag and an outside pocket on my pack. Probably a pain to understand when written out, but quite simple in practice. Allows for quick pack-up and deployment and no tangled lines.