I just had another thought: Find out which trail heads qualify for staying in the bp campground in the valley. If there are any with current openings on the date you need, get that wilderness permit now!
Yosemite ranger called back, since I left a voice msg yesterday, so I asked. The BP campground is indeed open to anyone holding a wilderness permit for any Yosemite trail head. Even JMT hikers leaving out of Tuolumne Meadows can stay overnight the night before in the Valley, and then catch the hiker shuttle to Tuolumne Meadows in the morning.
