I doubt your overflow is involved, Paul, and I assume you've made sure there are no obvious leaks around the tank or a fixture somewhere that's left on or faulty - is your black or gray tank filling quicker than normal; does it only happen when the pump is on on the highway, for example.
Check that your tank dump switch isn't faulty and road bumps aren't activating it enroute. I'm not personally familiar with the associated wiring, but if there's a valve motor and a relay or solenoid involved, I've had such things go awry on the road. With internal contacts that can carbon up, the carbon buildup closes the distance between contact points so that road bumps close them, activating the device they control. It may be bouncing on and off on the highway, and just not been on after parking, so you haven't noticed water dumping then.
As I indicated, I'm not experienced with the fresh tank dump configuration, but I'd start by maneuvering the water bay fresh tank dump switch to see if it operates normally and isn't oversensitive, activating the valve too easily such as when affected by road bumps. If it's OK, I'd then see if I could find the valve at the bottom outside of the tank; an associated motor may have a solenoid or relay nearby that I could check for over-sensitivity or obvious tendency to short.
Others here may offer more familiarity with the fresh tank dump setup and offer suggestions.
Joel