If I recall, the village at the west end of Twin Lakes is a privately owned campground with some cabins. Lots of fishermen and boats, etc. at Twin Lakes. Fish planted regularly.
So I think if you don't look to grizzled from your hike, you ought to be able to get a ride down to the 395 and then to Lee Vining and Tuolumne Meadows.
You might consider doing the opposite -- park your car at Twin Lakes, then hitch to TM before your hike.