I don't see an issue with the extra person and I don't think you need to "hide" the extra person (not having everyone outside at the same time, etc.). The limit is mostly to minimize the partyers - either adults or teens. With the varied ages of the kids, I don't see them being obnoxious or annoying to other campers.
Adding an extra amount for the extra person is always nice. I would simply divide the nightly fee by 6 and add that amount for each month. For example if they charge $36 per night for up to 6 people, the extra per person charge would be $6 per night That seems reasonable and isn't throwing a bunch of money at them as a bribe.
