I would say check every day even though it says it's all booked someone might cancel and get lucky
If you haven't reserved a campsite by now it's probably not possible.
Check the website to see if there are any open reservations.
Since the park fills up on non-holidays regularly, its gonna be full for the 4th. In the past when my family has wanted to camp there but couldn't, due to no availability, we have opted to camp in one of the neighboring private RV parks. There are several in the area with access to the river. That would be my recommendation.
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