Jungle hammocks work well on the chickees. Sometimes you gotta hang diagonally acorss the smaller singles, and sometimes you are hanging right on the edge, half over the water. But, if you are comfortable with "tree tents" you probably won't mind the latter. If you gotta go diagonal, just don't set up till sleepy time.
Hanging in the trees is another story. I believe it is frowned upon to "tie anything to a tree", I know that is true in the Fl State Parks. The biggest issue is first finding two trees that are the right distance, and that don't have any other trees or branches in the way. Cutting away those other branches is definitely a no-no as they most probably are some sort of mangrove, which are federally protected species. Cutting any live wood is prohibited anyway, I think. However, the biggest challenge is finding two trees stong enough to support you. As mentioned above, Red Mangroves (by far the most common along the creeks) evolved to withstand hurricane winds and tides... so they bend very easily. It takes two rather old and impressive red mangroves to support the average person in a hammock.
Using your hammock on a ground site is very do-able, without trees, if you bring two poles to act as the roof support and a ground pad. You make your hammock essentially into a bivy and sleep on the ground.
Well I tested out the hammock on the ground in my backyard, doable, but definitely need some work to see exactly how to set it up in a way that will stand up well to inclement weather. It seemed kinda flimsy and I couldn't exactly figure out how to really tighten it down cause the stakes kept pulling outta the ground.
Many of the places that you can hang a hammock are places you may want to avoid. Mosquitos are tolerable in the winter, but the closer you get to foliage, the worse they will be. You'll be setting up your hammock right in their power zone.
You can get a decent tent for under $100 that won't take up much more space than a hammock. I use one of these, http://www.campmor.com/outdoor/gear/Product___23889 it works great for ground and beach sites, and with a little engineering would work on a chickee.