Regarding access to rivers via navigation rights. It depends on the state. From what I have read in CO if you own the stream bed you own the river. Floating on the river can be treated as trespass. I read this a good decade ago so take it with some salt.
And what is considered navigable is debatable as well and will depend on state and maybe Federal law. What applies in one state might not be the law in another. Check a local legal beagle.
Back to the main subject.
If your post is on his land I think you have a problem.
Our land has a gravel road up the middle of the property. The property was subdivided into lots of 5ish acres but the land does not perk very well so it can't be cheaply built on. The developer lost some money on this 20-30 years ago. The first thing I did when we close was to put up a cable to block access. Eventually I put up a more permanent fence and gate. Because of the lay of the land and the road two sections of board fence 8 feet long and two 10 foot pipe gates work to close of the road.
Where the gate/fence is located I own the land on both sides of the road. People can and do come up to the gate. If it is open they will sometimes drive up to our house even though it is a GATE with several posted signs.
But since We own all of the land past the gate nobody has a reason to be up on the road. And we own the road. The lot lines go to the center line of the road.
If your "neighbors don't own land off the road I don't see how they can use the road. If you own both sides of the road I would just gate it and move on to the next set of problems which will be keeping the idiots off your land. I have cleared some of the property lines and I have put in T posts to mark my corners. Someone stole my T posts. They did not tear down the posted signs but they stole the T posts.
I have not decided if I will buy longer Tposts, say 8 footers and drive them four feet into the ground or just buy long lengths of rebar to put in the ground. The rebar might be easier to drive real deep.
Good Luck,
Dan