The snake skins that you were using at the RRG were the smallest diameter skins I have ever seen. They certainly make a nice, compact tarp when skinned.
I have been thinking about making a 1 piece skin like yours that is attached to the inside of astuff sack, sorta like a BB sack for a tarp. You would open open the stuff sack and would have a skinned tarp stored inside. One of the guy lines would exit out the back of the stuff sack, just like a BB bag. Tie that line to a tree open the bag and pull out the skinned tarp and tie to the opposite tree. You would slide the skin back to deploy the tarp and the unused skin could be stored in the stuff sack. Is that clear as mud?
I understood that. I like the idea. If you want to leave the tarp skinned but in some long coils (e.g. tucked under the top flap of your pack) you could that and just tuck the enclosing bag with it, or pack it up neatly and hang from its drawstring on something.