At the Florida state parks I’ve always been asked for my phone number right off. They didn’t seem that interested in my printed reservation sheet. I suggest you call the campground directly and see what can be done that way.
I found out that while Reserve America charges a cancellation fee, if you show up and cancel (we cancelled several days of our week reservation recently at Anastasia State Park) then there’s no penalty. At least that was our Florida experience.
Also on our recent trip we were chatting with the ranger at a federal campground, and he was telling us about someone who was staying at the campground and needed to leave early. Someone else just happened to walk up right then to ask about open sites….it was all worked out.
Of course this has all been in person so might not work in your situation.
