Hey Douglas!
There is a parking lot at the Crescent Meadow TH and as far as I know there are no restrictions on parking there during your backcountry trip. There is also a shuttle that runs out to Crescent Meadow. I’d check with the NPS to get the real details, though.
https://www.nps.gov/seki/planyourvisit/parktransit.htm
As for resupply, I’m drawing a blank. According to GaiaGPS it’s only 16 miles between Kern Hot Spring and the Tyndall Ranger Station, but you are about as far away from a trailhead as you can get. What is the route you’re taking?