Depending on the amount of driftwood that is washed a shore, and the size of it, you could just hang from it. I have done this in the past and have had to get pretty creative with it, but have done it.
You may need to carry an "extension" kit, for such an outing. Mine has 2 6ft whoopies, and 2 double ended (loops on each end) 6ft tree straps in it. I use the Warbonnet suspension system which is already 15ft tree straps.
Best of luck to you, let us know how it turns out.
My hammock set up is the grey DangerBird..