I use the hex tarp, but having played a bit with the HH asym tarp that came with my son's expedition, I'd say you can hang that tarp seperately from the hammock but still get good coverage.
Hang the tarp as close as you can to the hammock ridgeline. As others have said...if the weather looks bad, have a good, steep angle on your tarp, and make sure that you're perpendicular to the wind, to minimize rain possibly coming in on the ends of the hammock.
I've not used the tarp prussics/hooks on the HH ropes personally, because I don't care of the sag created when I get in the hammock. I just make sure to hang my tarp as low to the hammock ridgeline as I can to minimize the gap created when I climb in the tarp.
If weight isn't an issue for you...I personally like having a larger tarp...but that's just personal preference between which you prefer...better tarp coverage or minimizing your pack weight.