All of the above suggestions are good. Plus:
BOTH in separate skins. That is what I did for a couple of years, and there was really no problem with it, except the very small amount of extra weight of extra skins compared to a hammock stuff sack.
I would skin my tarp in one set of skins and hang it 1st if it was raining, or leave it hanging in the skins if good weather.
In the other skins, I would put my HH and HHSS after removing the pad, which went in a dry sack with other stuff.
This all made for a very fast set up and break down. Maybe not the absolute fastest, but plenty fast. And it left me the option of leaving the hammock in the skins if I needed more room under the tarp.
This worked about as good overall as anything else I do. Another way I like to go is tarp in skins, and hammock and entire HHSS including HH pad/space blanket ( or a PeaPod or UQ) and maybe even the top quilt still inside the hammock all stuffed down into their own large stuff dry sack or into my pack. Mostly these days this is what I do. On my most recent trip, I did this with a Claytor No Net hammock, PeaPod and Golight UQ plus a down vest all in one large compression (Event bottom)dry sack. Worked pretty good!