NY State Park Pass Policy

I'm thinking of taking the family for an overnight to Stony Brook State Park in August. Originally the plan was to do Letchworth, but they have a 2 night minimum. My question is, if we leave Stony Brook early enough, would we have reciprocal access to Letchworth similar to how the DEC campgrounds are run?

If so, would we be good for the day or only until the 11am checkout time?