If you have the luxury of going ~100 miles, you need to get to the High Sierra! No better place than Sequoia-Kings Canyon.
I believe the following is about a 90-mile loop:
Roads End (Kings Canyon NP),
over Avalanche Pass,
up Cloud Canyon,
over Colby Pass,
east to the PCT/JMT,
north on PCT/JMT over Forester Pass,
continue north over Glen Pass and through Rae Lakes area,
exit Woods Creek (west) back to Roads End trailhead.
If you are falling behind on your schedule because of the insane ups-and-downs you'll be doing, this route has the benefit of a bailout option after Forester Pass. (Return to Roads End via Bubbs Creek; saves about 20 miles overall.)
If you are open to offtrail hiking, then it's a whole different ballgame. In that case I'd recommend a shorter trailed loop, with a lot of x-country layover-day options, such as Evolution Basin.
If you are REALLY good at offtrail hiking, you could do a section of the Sierra High Route. Just leave your car at Bishop, hitch to North Lake, trail over Piute Pass, offtrail to Sierra High Route, walk as far as you can for 3 days, then exit and hitch back to your car in Bishop.
Post over at highsierratopix.com and see what they tell you there.