Your chances are very good. You have the correct time to show up, so I am sure you have been reading all the hints.
And understand that the Unused Permits numbers that are
shown here are the numbers at the end of the day for the date of entry. The number of no-shows on any given day are always quite a bit more.
And keep calling in this week. Most people who call in and release their reservations do so in the few days just before their hike.
When you go in on the day before to ask about no-shows, also ask about hiking that same day. They may still have some available for the 16th.