I’ve driven coast-to-coast in the US six times and many more times on trips of somewhat shorter (but still multi-day) duration. I’ve never been questioned or harassed for sleeping at a designated rest area off an Interstate (plus they’re somewhat more heavily traveled, lit and policed in the first place), but the one time I tried to park in a gas station parking lot (when the place was closed for the night) I was awakened by local police a couple of hours later because they were afraid I had gone to sleep with the engine running and that I might be overcome by CO fumes in the closed car—a valid concern.
I would recommend that you:
1. Fully exit the highway or roadway and park completely off-road somewhere;
2. Put a sign in your windshield that states clearly that you did not leave the engine running (so they’ll know you’re really sleeping, and not dead or unconscious);
3. Include a note about when you stopped and when you plan to resume travel, and
4. Lock the doors.
The police aren’t trying to hassle you, I think, as much as to ascertain that you’re NOT dead, unconscious or drunk.