If you look on the DEC info locator, you'll see that while ~75% of the shore is public, all the land associated with the road is private except for the roadway itself, the only road access is through the campground. Adding the parcel map, it is possible that the roadway ROW ends at the lake, what you can see from the turnoff for the Moose River Plains, but my recollection from checking it in the summer is there is no parking there, and it is posted against it. You could check with the town on whether you can access from the ROW, but I think you are still going to be parking up by the campground or the plains gate, and its still downhill to the lake.