That's a pretty short/fast trip! It sounds like you only have 2 nights to camp. You are hiking out of Kings Canyon, correct?
Since there is so much elevation gain, be sure to pack as light as possible.
Although I have not hiked up beyond Mist Falls, I understand the Paradise Valley area is beautiful. You're in for a treat with the swinging suspension bridge where the JMT crosses Woods Creek.
I think the Rae Lakes is one if the prettiest places on the JMT -- I'd like to go back one of these years. If you can make it all the way up there on the first day, it would be the most rewarding area. I think there is a rule that you can only stay one night by the Rae Lakes, though.
I camped on the JMT about 3-400' climb above the highest Rae Lake. There is a nice bench with trees and a campsite protected by the trees. We hiked from there, over Glenn Pass, and all the way to Roads End in a long day. That might make a good last night spot for you. After the Rae Lakes, I felt the Bubbs Creek trail was anticlimactic.
