Upper Boyscout is the ideal place to overnight, IMO. Some people will try to pack all the way to Iceberg, but that gets them high enough that sometimes AMS symptoms will hit while they sleep.
I really like your idea of heading directly to Horseshoe Meadows for the first night. If you could do that, then come back down to Lone Pine to try for the 11 AM walk-in permits for the "
J34 NF Lone Pine Creek Overnight", it would be perfect.
If you don't get two of the four available walk-ins, you should ask about the no-shows for that route. I think they become available something like 10 AM the day OF the hike. (So you could also get lucky and get no-shows for that very day.) That time may be 10 AM. Call to find out for sure.
And if you DO get the walk-ins for the next day, you might head north to Independence, and go up the road to Onion Valley. A day hike to Kearsarge pass would give you a 2000 foot gain and fantastic views. Or go farther up to Toms Place by Crowley Lk, then up to Rock Creek road's end and hike in that area. Both options would add to your acclimation.
If you don't get walk-ins or no-shows the first day, plan on a second try. I can't imagine your being unlucky two days in a row.
I didn't mean to imply anything by pointing out the Orientaton notes. Many people miss them, that's all. And I hope you found the
Mountaineer's Route info links within...