No, I wouldn't "click and see". I would first check the availability page. Make this link your top bookmark or home page or something. Then if you see anything available on your Aug 10 start date, go to Update Reservation very quickly and go for it.

But also remember, if you don't get a permit on May 1, since you are going mid-week, slots WILL open up. The no-shows are declared at 10 AM on Aug 10, so at the very least, if you are there on that date and time, you can probably add a person.