I did this last year: Mineral King to Whitney

Transportation into Mineral King is a major issue for a one-way trip. The HST (High Sierra Trail) is a classic crossing, and you can take public transportation to Crescent Meadow. TSX Challenge people guide groups from Horse Corral Meadow across to Whitney or Horseshoe Meadow. I've made the crossing from Onion Valley to Roads End in Kings Canyon as a day hike.

All the Sierra Crossings are special hikes to me. It gives me a unique sense of satisfaction to start on one side and finish on the other.

Looking at the trails of your initial proposed hike, it looks like a lot more than 45 miles. Lots of miles in gentle terrain east of the Kern. Tunnel Meadow even has an abandoned air strip.