Fee-free launch at Lake Cushman?

I've only fished Lake Cushman once, a few months ago, and was only able to find two launch/parking sites. One charged $10/day and didn't even open till 10am; the other was the Skokomish rec area which charged $7/day and officially opens at 8:30am but can often be accessed earlier. I went with the latter one and it was a great, non-sketchy place run by friendly folks. Nonetheless, it still kinda sucked to have to pay when there's a statepark up the road that the nefarious DiscoverPass should cover. I scouted around the park briefly but didn't see any promising trails down to the water. Anyone with experience in the area know if there is a way to get a kayak to the water from the statepark?