Here is the map

https://caltopo.com/m/2C1A

From Onion Valley over Kearsarge and Forester passes the distance to the Whitney summit is ~37 miles.
Form Horseshoe meadows via New Army pass is ~ 22 miles.

Both options are excellent and walk in permits are easy to get (you can also look for cancellations online to book in advance). The only problem is that you also need to get an exit permit if you want to descent from Whitney via main trail. If time permits (5-7 days), I would leave the car at Onion Valley or Horseshoe meadows, shuttle to the opposite trailhead and do the whole stretch. You will love it.