Another option to stay with the shorter tarp: what kind of rain gear are you using?
The reason I ask is that a poncho (one that actually opens all the way up along the sides, like the GI poncho or the GoLite poncho/tarp) can be rigged as an improv Grizz beak. Then, all that's needed is to pick a site where you can hang the foot end of the hammock into the prevailing wind and put the poncho up as the beak.
I've a short video on how I do that with mine (since making the video, I've added grosgrain loops at the shoulders of the tarp so that I can run some line from the bottom of the beak to the tree on that side if the wind is really blowing):
Hope it helps!