Stokell, it sounds like a great trip. You should read this article if you want some excellent insight into stealth camping.
http://www.kenkifer.com/bikepages/touring/camping.htm
Although I'm not greatly experienced in stealth camping, I've done a few trips using the stealth method. I find it superior to a campground even without considering the money saved.
Both my brother and myself use the same hammock you have purchased and we both love it. On our last weekend tour we followed a canal path along the Delaware River. We ended up camping about 20' from the river on the river's flood bank. There wasn't a place to set up a tent and even lying on the ground in a bivy would be difficult as the ground wasn't level. But with the hammocks and a couple of trees we had a comfortable spot to sleep. It was funny because we were so close to the trail we could hear the people running past on the gravel but they had no idea we were there.
A couple of things about the Hennessey Hammock.
First, It's a good idea to bring some tent spikes. At least two for the rainfly so that you can adjust the fly for good coverage. Another two spikes can be used to pull out the sides of the hammock bottom. I don't usually do this but it makes the hammock more spacious.
Second, The bottom of the hammock allows your body heat to escape. This is especially noticable if there is a wind. compared to a tent or bivy where you are on the ground the hammock won't keep you as warm since the bottom is exposed. This doesn't sound like it will be a problem in the temps you are looking at but you should definitely try the hammock out to see how much insulation you need to be comfortable.
Third, at first I had some problems stringing the hammock up. I've found that if I tie the cords at eyelevel the hammock is at a perfect height. I also had some problems with the ropes slipping down the trees as I moved around in the hammock. So make sure the ropes are nice and taught and securely lashed to the trees to ensure a good nights sleep.