Some questions.
What parts of the NE? The really hilly bits?
What experience have you had already with SS and hills?
People we know have done the Boston-Montreal-Boston 1200 randonnee, though places such as Vermont, New Hampshire and New York State, on fixed gear (and probably a few have done SS). And randonneurs go lightly loaded.
Remember also, having a flip-flop hub is all well and good, but then you have to be confident that the terrain you are about to tackle will comprise of quite a lot of climbing, and the effort to swap the rear wheel round and back again later will be worth it.
I've done FG touring and quite a lot of centuries with FG in various terrain profiles, and I've never had a flip-flop hub, so the gear I've had is it, and I survive quite well, knees and all. If you need to, just get off and walk until the climb gets easier again.
The advantage with a SS is that you can selected a moderately low gear for climbing, and get away with coasting down hills at a good speed.