My experience with the national forest campgrounds is that on the few occasions they are full, someone will let you share a site with them. Lots of people travel in RVs and aren't even using their tent pad & picnic table. Just ask, and definitely offer to pay or share the fee.

You can also approach the camp host and ask if they can help you out, I don't think they have to, but they usually do.

If you are a big group, this might not work for you, but for one or two people it probably will.