Although I coil
line I intend to stow that way, I generally coil frequently used sheets slightly differently. I start the same way and then when I have everything coiled, I draw a single loop of
line from the middle of the "pile", turn it 360 degrees around the middle, and then draw it up through the resulting "top loop", making a "handle" which can hang from a bungee loop in the
line locker.
While this isn't great for lying on the deck, if you are hanging
line from a hook or another loop, the weight of the
line itself will hold everything in place.