I am assuming the train from Kearsarge to Whitney is a well maintained one and one we can attempt w/o any x-country experience?
Exactly, which is also why permits disappear quickly on it.
But I'm pretty sure in late June you will have no problem with walk-ups. The only question is if they'll transfer your Whitney Exit when you do the walk-up. You could call the Inyo permit office and ask if they allow that when switching trailheads during pickup.
