I should mention this one big negative to the above technique, which will keep me tieing to trees with a larger hammock. When I used the "pull down and pre-sag" technique ( to make up a name for it), it helps greatly with many of the problems associated with hooking to the hammock. I even tried it with my MacCat and it worked ok plus some whopping rain coverage BUT:
When I do this, it add's a new problem: it makes entry into the hammock a real pain. It somehow makes it a struggle, with out going into detail. So I'll probably stick to normal use of my MacCat or Hex fly tied to trees. But, if I was a new user of the HH with ASYM fly, I wouldn't hesitate to do this in storms to be confident of adequate rain protection.
the key things about the technique are that the tarp go on the suspension line, and that there be a ridgeline. So it seems to me to be a method to keep in mind for any tarp, on any hammock with a ridgeline. Which of course includes top-loaders which would negative the issue you seemed to have backed into (sorry, couldn't help it... )