I started with my HH + tarp in the snake skins. But when I added the UC, the bulk was too much. I read a few posts on this forum and decided to just put the HH and UC as one unit in the snake skins and keep the tarp separate. That's because if it is raining (the reason I'd use the tarp), I can set it up first and work under it to rig the hammock. Also, at take down time, I can get things put away dry under the tarp and carry the wet tarp separate from the dry stuff.
Since then, I discovered that sun shield from Bliss. It's about half the price of snake skins and sort of like a tapered bishop bag (draw strings on both ends). It is larger than the snake skins, just a tab bulkier heavier - but I am not a gram weenie (I'd rather carry 80 lb. in my kayak than 40 lb. on my back).
So I may end up with the hammock + UC in the sun shield - a UQ may fit as well! - and put the tarp in snake skins. That way both parts have their wrapper and the wet is still separated from the dry.