I'd park in the lot right outside the Wilderness Center, or if it is full, the next big parking lot down the road towards the Lodge. The second and third lots from the right in the map below. Don't leave a trace of food in your car, stick a note on anything you store in the bear boxes, otherwise I can't think of any issues.
You can leave a car pretty much anywhere however long you like. In 2006 I left a car at Happy Isles for 3 weeks... when we returned we found a warning notice on the windshield, faded and about 10 days old. Got it as a result of a bear checking the car out.
We had cleared all the food out, knowing it would be there a while. Closer inspection revealed 3 packets of parmesan cheese in the trunk.
Thanks for the info....assuming I don't find an alternative to the shuttle, looks like I should just try to park near where it leaves from. As we are leaving Monday, I trust Tuolumne will be a bit less of a zoo.