I'd go research the local laws. You are saying Park Ranger, is it a Federal Park? If so, make sure you dont get in trouble with a Federal Park Ranger, they carry guns and have broad federal powers. A ticket from a Federal Park Ranger has to be settled in Federal Court and you have to go stand in front of a Federal Judge.

If its a local park, go talk to the local people. Find a someone in charge and explain what you want to do, and ask their advice. I've found most people are very helpful if you approach them with a problem and ask for their advice or assistance.

I suspect that if you leave your car on the road, you might have less issues with the ranger, use the beach wheels for the whole trip from the road to the water. Or if he shows up next time, ask him what is allowable.