Good Luck, DUG! Hauling that much food up out of Whitney Portal will definitely slow you down. Even with superlight gear, you'll be hiking with nearly 30 lbs on your back. The thought of racing against time for that many days with that kind of a load...
And I wouldn't worry about the medical coverage -- it is not often that you hear of distance hikers needing medical attention. It's on the most heavily traveled trail in the Sierra. How dangerous is that?
If you go in July, you will be just behind all the northbound PCT hikers. They usually head through about mid-June.