Dolface, I hope you are aware of the number of unused / no-show permits that are usually available. (See these posts:
2007 and
2008 )
You really should not have any trouble if you show up at the Visitor Center at 11 on the 23rd. No-shows for the 23rd come available then, and cancellations for the 24th also come available.
...and they are free!
See step 6 of V.Fred's Wilderness Permit Options information (link is above on the left in the Feature Topics box).
And last, if you really want to pay the $15 reservation fee, I would guess most cancellations come in no more than a week before the hike dates. So call several times a day during the week before, and you will probably be successful.