If you can plan on a layover day at high altitude, it would be a smart move. I would recommend up above Guitar lake.
Don't stay at Guitar or the small lake above it. Push on to the sandy shelf above the small lakes. It is spring feed and from here you can hike over to Hitchcock lakes. Also, from here you are at 12,000 ft and as close as you can get for your run on Whitney.
No one seems to stop here and the fishing is great. We were there on August 20th and pulled a 12", 14" and six 8"-10" Golden Trout out.
Pan fried in olive oil, cornbeaded. Man what a treat.
The only downside to this location is that if a storm comes in, you'll be slammed.