LOL.....Contracts and Clauses over a campsite rate increase? Really?
I guess the OP could travel from TX to NH and file the paperwork to go before small claims, the magistrate, or whatever they have in NH, then travel back when it's scheduled? Who knows, maybe NH has same day walk in service at the local court.
Maybe find a good attorney in NH, or send one up from TX, and sue them. Cost effective that is.
I'd bet they have a published policy for this situation, and a lot more people than the OP are in the same boat. Maybe they don't but it matters little one way or the other. They can pay the $80 or not out of principal and find somewhere else, someone else will take the site if the OP decides against it. No amount of RVnet strong arming is going to change anything.