What about Grand Haven is the attraction?
If it's a site on water you're after, there's more attractive parks that may be easier to get into.
If not, most parks along the expressway and lakeshore are very very difficult to get into for July. Tens of thousands of visitors and only a few thousand campsites.
Moving away from the expressways makes your chances a lot better.
I should add, if you're self sufficient, overnight parking is permitted and water hose taps are available at the Manistee beach, only ninety minutes North. You're not on the beach but it's right across the street.
2013 KZ Sportsmen Classic 200, 20 ft TT
2020 RAM 1500, 5.7 4x4, 8 speed