This is the mineral king area. Should be very quiet. It is apparently almost always very quiet because it is very difficult to reach. The payoff, however, is awesome. Trails are much more rugged than in main park from our experience.
Our overnight route (Very beautiful, we stopped at cliff creek and you will probably be physically stopped here as well.)
sequoia grove (This is the sequoia grove we were trying to get to and one of the few where you can camp under the giant sequoias. However, this may be impossible to reach due to river heights.)