I think installing valves on the overflow tubes is the solution. This problem has been around for years and hundreds and probably thousands or tens of thousands of people have installed valves on their overflow tubes.
The only time the valves are closed is during travel. I open them when I fill (so the air can get out as the water goes in) and I open them when I arrive at the campground (so the air can get in as the water gets pumped out).
For those who say: "But when you forget to open them you will have big problems" well that may be true. But if it is part of your set up and take down, it becomes routine. I might forget to hook up my safety chains. I might forget to retract my awning. I might forget to put oil in my engine. I might forget to put on my pants before I go out for a hike. All these things might cause big problems but we routinely do them and they become second nature.
