SCastle, I just checked Recreation.gov for overnight permits
(Link). There is currently ONE overnight permit available for 7/14.
Try clicking the link above; it should take you directly to that page (you may need to enter the group size = 1).
Otherwise, you should be able to pick one up the day before, as groups picking up their permits often drop people from their numbers, so those become immediately available at the Visitor Center. If you walk in and talk to the permit clerks, they will be able to help you out. If at first there isn't one available, keep checking every 15 minutes or so.
