Try Langley via the Cottonwood Lakes TH. I'd recommend maybe doing a 3-day loop!
Day 1: TH to Cottonwood Lake 3 or 5 (about 5 mi and 1100' gain).
Day 2: Lake 3 or 5 up Old Army Pass, drop your overnight pack, climb to the summit of Langley, return to the pack, descend via New Army Pass, camp at the lakes at the base of NAP.
Day 3: NAP lakes to TH.
If you don't like the idea of humping your pack up OAP and NAP, then just leave your base camp where you want it and day hike up and down Langley.
Langley's TH is 1700' higher than the Portal, and her summit is 500' shorter than Whitney. So if the short first day leaves you with too much energy you might even consider doing the short climb up Woollyback, a sub-peak of Langley that hovers above the Cottonwood Lakes basin.