Training for a backpacking trip is over sold. It actually takes very little training. The hardest part of your trip will be going 6-miles, +3,700' under a pack load. This isn't easy but it ain't 22-miles, + and - 6,000'.
I'm big going and learning. If you fail, you fail. The mountain ain't going anywhere and you would hopefully learn from your mistakes.
My guess the switchback will have been forced by late July. Which means you will still be hiking on snow to some degree...there is always snow/ice at the cables.
Personally, I would push my daily train out to at least 5 days a week, 6 is better. I run to keep my legs in backpacking shape. Figure a good hard 4-miles a day would do you good. On your last weekend, I'd fill my backpack up with what I was going to have and day hike from Angelus Oaks to Limber Bench in the San Gorgonio Wilderness, if you are a SoCal. This is about the same profile as WP to Trail Camp. If you can't make there, you have to have a good long conversation with yourself about heading to Lone Pine.
