Third option: On Aug 5 when you are trying for the Aug 6, see if there are any no-shows for Aug 5 (they are declared at 11 AM Aug 5, I think). If there are, and no Aug 6 are available, use those, hike up to Lower Boy Scout Lk, and camp the first night.
Steve, I'm not sure I understand. Are you saying we can get an Aug 5 overnight permit and all camp overnight at Lower Boy Scout lake? Some in the party would have Aug 5 overnight permit(s) and some would have Aug 6 overnight permits? Is no permit required there? Also how about this: can some one get 2 Whitney day permits - 1 for Aug 5 and 1 for Aug 6 and use those to go on an overnight hike up the Mountaineers Route? If checked by the Ranger a valid permit for either day could be shown?