I do something similar. But turned round the other way.
When I attach the tie out lines to my tarps I put the taught line hitch loop at the tarp end and attach the other end of the line to the ground stake with a loop , or more recently with the Pile hitch.
When packing up, I disconnect the line from the ground stake. Close the the taught line hitch till the loop is only open about 3 inches. Just open enough to easily stick the coiled line inside the open loop. Then figure 8 the line on my fingers, as described earlier. Stopping about 4 inches from the taught line knot.
Then roll a few inches of the line around the middle of the figure 8 coiled line. Rolling the coiled line toward the TL hitch. Then just turn the coiled line and tuck the coil inside the the loop. Then tighten, or push the taught line knot toward the tie out loop on the tarp. This holds the coiled line inside the loop. Thus the coiled tie out line is snugged next to the tarp edge tight to the tie out loop or d-ring. Then just stuff tarp and all into the stuff sack.
This method doesn't weight anything, there's nothing to loose, and when I need to adjust the tightness of the line with the tarp setup, my sliding adjustment knot is up off the ground, easy to reach. I can also reach the the knot from underneath the tarp when its raining , if I need to tighten the tie out line, with out going out to the stake end and getting wet. Or at least most of the time, if the taught line knot is not to far away from the tarp edge. Which is usually the case when I expect rain and the tarp edges are down low and not up high tied to a tree limb or hiking stick to give me a view out to the woods.
Anyway, works for me. ymmv.
Also I might note that I use tie out line that is a bit rough in texture, not a slick feeling line. The rough texture increases the friction of the sliding knot, helps the knot hold better and not slip when in use or when everything is coiled to pack away the tarp.
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