Since you will be coming from the east side after Whitney, why not avoid the Valley altogether? Instead, you can check in with the Tuolumne ranger station and see if there are any walk-in permits available.
another east side option:
you can even do Half Dome as a day hike from Tenaya lake. MUCH longer route, but doable. You can do it going through Sunrise and JMT, or, over over Clouds Rest to get to Half Dome. Again, it is MUCH longer, but doable.
