That road (Andrews Road) has been around for 100 years. Before it was called Andrews Road it was New Road, and the bridge where you carry the Kayaks across was called New Bridge. You can see that on the Burlington County South map that Ben has on this site. It is a right of way that passes between properties on both sides, some private, and some state.
My property records do not make it to that part of the lake, so I can’t come forward with proof that the road is public. But lets look at it from this point of view. The bridge next to the Pleasant Mills church is public, but they have closed it off for various reasons. One the bridge is not in great shape, but I can bet you the church was not happy about vehicles passing that close during service, or for that matter at any time. So they closed it down.
I say the same happened at Oswego. He didn’t want vehicles traveling down it, the state most likely was tired of policing his property around the lake, and as I mentioned the feds did not want vehicles there either. So they put up a gate and all involved are happy. Just like the gate at the Pleasant Mills church.
With that said, I still would make sure you have permission from whoever you feel is the owner. And if they say no I would take that as the final answer.
I will do my best in the coming months to get proof of ownership of that road at the gate.
Guy