Any hints to score a reservation on Recreation.gov

I don't think you can go by a clock to know when to hit the book button, as the clock you are looking at is probably different than the one Rec.gov is using. What I do is start hitting the Book Now button a little before and if you're too early it kicks right back to the page where you can the button again. Repeat as fast as you can! I've had fairly good luck with this approach.