Sara, don't turn them back in just yet! I would talk to the Wilderness Permit office again and ask about switching the unneeded permits to the earlier day (IF an open slot shows up). You could ask them whether, when (and if) you spot an opening for July 7, if you called them at that time, if they would help you switch so you had three permits for the earlier day.
I think they might be able to do that for you, or you might even be able to switch online (but I doubt that). Also, due to the crazy mess-up, they might accommodate you and add your third friend as an alternate leader on the unused(later) day permit, so she could in fact have a sure-thing permit.
And, with that sure-thing permit, when you and she show up at the Visitor Center in Lone Pine, they WILL switch you to the earlier date if a slot is available (I keep telling you they will likely have some available.)
By the way, when you talk to the WPO person, please tell him (or her) that neither the rec.gov or Inyo N.F. web pages specifically state that you do NOT need multiple overnight permits to stay multiple nights in the wilderness. It is such a well-known fact by them and all of us regulars, that everyone has fallen into the assumption that "everyone knows that" already. Your experience demonstrates the need for a sentence or two explaining that.