How should I handle a highway patrolman who stops me occasionally to give incorrect instructions about my riding duties?
There is no one size fits all answer to this, except the first point below. 


When dealing with police, or other authority figures, always behave respectfully. 
Contact the people responsible for sweeping the road and ask when or if they are going to do it next. Maybe they only sweep when requested. 
Find out if there's a local bike advocacy group. They would have a history of such contact and possibly have established communication channels. If they exist then talk to them. 
Failing that, then get dressed in a suit or other best clothes, and drop in to the police station with your bike to talk with the duty officer, probably a Sgt. Explain what the problem is and how you've dealt with it. Also explain that you're not complaining, just would like to not get stopped regularly. Also ask if there's a specialist cycling officer to talk to. And make sure you ask why it's happening, to get the story from their side. Do not create a you-versus-them situation, because they have the power and you lose. Once the discussion is started you can show what a sensible and reasonable citizen you are and get them on your side. It's possible that a motorist or some senior member of the community has complained (not necessarily about you), or that they have received a directive from higher up. I guess the point here is don't go in expecting them to suddenly roll over. Look for common ground and understanding.  
Invite the police to come for a ride with you. Of course you would take them along that stretch of road. 


Good luck.