I used to try to do that - the groundsheet thing.
Now I just loosen the laces on my trailrunners and pull the tongue out towards the toe for 'bedroom slippers' and stick my feet in those when I want to get out of the hammock. My pack hangs from my hammock suspension (with dry rain gear in it). Anything else I have is either food/firstaid/stove in the bear can/ursack/food bag or I'm wearing it. If I have wet rain gear it is on the suspension also. In the unlikely event I have spare clothes, they are tossed in the hammock.
Sometimes, I still bring a scrap of Visqueen plastic just big enough to go under and over my pack, but it is too slippery to try to stand on.