You are correct that a Statutory Road Association is for road maintenance only.  A Homeowner's Association or a Non-Profit Road Association can spend its funds on other things like maintaining a dock or beach area.  You are also correct that a Statutory Road Association can set up a fee schedule where different categories of owners pay at different rates.  For example, some associations charge at one rate for developed lots and another for undeveloped lots, or one rate for seasonal homes and another for year-round.  You could potentially charge a different rate for all rental properties, but I think you would have a hard time justifying how a renter causes any more wear and tear than the owner.

What might be more helpful would be to see if the deeds to properties on your road refer to a subdivision plan or to any sort of covenant.  If so, look up that document on your county's Registry of Deeds website and read it very carefully.  Sometimes those documents will include limits on what can be done with properties.  For example, they may say no businesses other than a cottage industry.  You may find that there is some restriction that would prohibit a rental.  If not, I don't know if there is much you can do.  One thing that might be helpful would be to amend your bylaws to say that any damage to the road beyond normal wear and tear will be billed to the landowner.