I can't speak from any experience regarding hammock camping in the Presis - but I expect it will require a decent amount of descending to find places to hang. Even once you get below treeline you may have to descend quite a ways for the trees to be tall, spread out and strong enough to hang. They are quite gnarled and thick for awhile. I have not yet hiked the Jewell Trail.
One option to do the hike as a three day is an easy day 1, taking Valley Way to the campsite below Madison Springs Hut. Then you start Day 2 pretty much at treeline. After hiking the entire ridge on Day 2 you could camp at the Neuman tentsite or somewhere down the Crawford Path. Then it's a short hike out on Day 3.
Another option other than Jewell Trail is the Caps Ridge trail which heads down from Jefferson. I took this trail last month and
you can see what it looks like here. Obviously it will look very different without snow but this was about 1.5 miles down from the Jefferson summit and will give you some idea of what the woods look like at that point.
General advice for doing the Presi Traverse: as you seem to know there aren't a lot of water options. You'll be able to fill up at the Madison Springs Hut and that's basically it until you reach the Mt. Washington Summit, which has potable water as well as a cafeteria, amenities and lots of tourists. The Lake of the Clouds hut is close to Monroe and that's another place to fill up. Everything north of Mt. Washington is essentially a massive boulder field. There is dirt/rock trail at times but you'll be doing a lot of rock hopping which may slow you down considerably based on your confidence, skill and pack weight. There's very little in the way of shelter above treeline and bailout routes could potentially leave you pretty far removed from your cars so weather knowledge is important.
South of Mt. Washington the trail becomes much easier. Rocky steps will lead down from Mt. Washington and and after that it's mostly easy graded dirt trail/rock slabs on the Crawford Path. Things get a little more technical going up Monroe and Eisenhower but nothing compared to the northern presis.
There's so much to do/see up there it's hard to give suggestions for other things. If you end up finishing with time to spare on Day 3, Arethusa Falls Trail is only a few miles south of the Highland Center on Route 302. It's an easy hike that leads to a splendid waterfall, depending on how the water is flowing. And the Saco River flows alongside Route 302 - one of my favorite things after a hike is stopping at one of the many pull-offs and soaking my feet in the Saco. The more popular spots have great spots for taking a dip. Great way to wash off the funk.
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