Ok, keep hitting this link (make it your home page temporarily), and see if any come available just a few days before.

Otherwise you have a pretty good chance of snagging them as a walk-in request.

When I was there last week, there were ~30 people there looking for walk-ins, but that was for all trails. They have everyone pull numbers, and lowest numbers go in first to try. But no-shows for Day Hikes come available at 2 PM the day before, so if you are there then, I think there is another mini-lottery to see who can go in first.

Good luck!!!

By the way, you have a very good chance of getting what you need, since mid-week permits are most often available. Check the unused numbers.