Just extend the overflow line to a higher level, maybe up around the top of the back window. I think you're getting siphoning action that drains the tank while on the road.
A shut-off is potentially risky because you might forget to open it and rupture the tank when you fill it.
The other option would be to put a solenoid valve on the overflow, connected to a sensor that figures out you're filling the tank, so that, while filling it vents appropriately, but once filled and the line disconnected, it closes the vent.
If you have pressure fill of your PW tank, rather than gravity pouring, a pressure switch on the inlet line would do the job.
Frank Damp -Anacortes, WA,(DW- Eileen)
ex-pat Brits (1968) and now ex-RVers, as of 08 Dec 14.