I was able to book a site in April fairly easily. I think the key was my choice of Sunday through Friday rather than a weekend. The weekends were booked almost immediately.
One thing to note, if you are larger than 35', there are only 12 sites in the valley that will accommodate you.
And try going through recreation.gov. There is a delay when using reserveamerica.com to transfer you to recreation.gov.
Also, if you look today, you can see which sites are already reserved past the previous booking window. This may help narrow down which sites you try for.