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?
I am saying: You go, planning to spend ONE night, Aug 6, in the North Fork area, climb the MR, then hike out. BUT, on Aug 5 at 11 AM, if you aren't able to snag the 4 walk-in permits (because someone else drew a lower number out of the hat), there just might be some no-shows (out of the 6 reserved) to start the hike on Aug 5. So, you decide to take those. It's already 11 AM, so you go to the store and pick up more rations for another dinner and breakfast, head up the North Fork starting late -- 4 PM would even be ok, since you can make it to Lower B.S. Lake in under 2 hours. Eat dinner and make camp.
...Next morning, wait for other hikers (or even hike down without the pack) and walk in again with the hikers with the Aug 6 permits. On Aug 6, everyone hikes up to Upper B.S. Lk or higher, and makes camp. On Aug 7 everyone climbs to the summit.
And you could then spend another night in the North Fork area -- Once you get INTO the area on a valid permit, you can stay indefinitely -- only you have to move every 2 weeks
Getting multiple day permits isn't a good idea. Ranger can see you are carrying overnight gear (or find you at your camp).