FYI You can not practically or legally drop down off the ridgeline on all side Trails.
https://www.fs.usda.gov/Internet/FSE...rdb5363715.pdf
Generally when going from South to North, taking any path to your right puts you in nasty territory and almost always in wilderness area so you need to be 200 feet off the trail. In many cases you are losing a lot of elevation before you encounter anything suitable to hang a hammock.
Ir you take a left, Edmands Path has suitable trees about1/2 mile down the trail and water along the way.
Ammonoosuc Ravine Trail is no camping all the way down to past Gem Pool. Its long long way down.
Jewell Trail has some rough camping down below treeline but its very exposed and the trees are small,, my guess you are on the ground.
There are no good options off of Jefferson, they are all very long downs.
As mentioned RMC has some legal sites that get mobbed on Adams.
Great Gully is no where you want to go unless an uncontrolled fall is on your list
Valley Way campsite is mobbed all the time. There are some trees downslope on a steep slope that would work for hammocks.
Howker Ridge and the Daniel Webster Scout trail are both very long hikes down.