TwoFortyJeff, I'm planning a trip from the Giant Forest (starting at the General Sherman Tree) to Yosemite Valley too, except that I'm starting in August not earlier like you are planning to do. I have been planning to do this trip for the past several years, but one injury or another has prevented me from completing this trip in the past. Here are some inspiring and fitting words from a legend of the High Sierra:
"Giant Forest is the starting point of the High Sierra Trail to Mt. Whitney, a well built trail about 48 miles long, passing through a high region of great beauty and scenic grandeur to meet the Muir Trail at the headwaters of the Kern River. It seems fitting that the trail should be made a part of the official Muir Route, for it would add both to its length and to its attraction. John Muir loved the great trees as much as he loved the high mountains. The John Muir Trail would then become a High Sierra Route from Yosemite Valley in Yosemite National Park to Giant Forest in Sequoia National Park via Mt. Whitney, having a total length of about 260 miles, and would traverse most of the finest and grandest regions of the High Sierra. I wish to suggest and urge the adoption of this as the official route of the John Muir Trail."
Walter A. Starr, Jr., Starr's Guide to the John Muir Trail and the High Sierra Region, 1934.