Minimum distance concerns is why I have continuous loops connecting the hammock to whoopie slings with a Dutch biner. I use Elephant trunks or Dutch buckles instead of a MSH so should the need arise, I can ditch the whoopies all together and simply loop the continuous loop from the hammock around the Dutch buckle or onto the Elephant trunk.
These two methods allow some adjustability so you can still fine tune the sag. I think the shortest I can go form the hammock to the tree is about 8 or so inches. Now the other problem of course is the length of your tarp's ridgeline. You can't go short if you have a large tarp.
Don't let life get in the way of living.