there is definitely an availability API. I helped lobby for it! We also implemented it at Hipcamp (If you can't find a signup form on the rec.gov website just

there is definitely an availability API. I helped lobby for it! We also implemented it at Hipcamp (If you can't find a signup form on the rec.gov website just contact them directly and ask for access. I think their team was rolling access out slowly as they hadn't finished building a fully fledged login system but last I checked they do want 3rd parties being able to build on top of that data)