Since you are asking whom to contact, I assume the sign is just a sign, with no "by order of ......"
I also assume the Carova ramp is not heavily used. If it were me, I would just park when needed.
In my experience asking gets a no 100% of the time. Not asking gets ignored more often, as long as you
are not obnoxious about your parking location.
It's patrolled by the Currituck Sheriffs Dept. My experience with the Deputies on Carova Beach has been very positive...and Ive had experiences with law enforcement agencies around the globe!
These guys go out of their way to be a part of the community, take the time to get to know us locals, etc. I'm pretty sure if I was to call the Carova Beach hotline and let them know that I was headed over to Knotts Island to help out the an elderly couple and might be there a while I'm pretty sure they would be cool about it.