I confess I'm baffled as to why one might fear filling the gray-water tank. That is what it is for.
My 21 foot TT has a 25 gallon gray tank. It takes AT LEAST a dozen showers to fill it if you do nothing else. A 3-5 gallon shower is what is called a profligate and extravagant waste of both water and propane to heat said water. You can get clean with only a gallon or two if you even half try.
We empty the gray tank a couple times a week, my wife and I. The ONLY time we've ever filled the gray tank completely, it was because our visiting daughter did the dishes and thinking we had the dump valve open, ran water the entire time for rinsing the dishes.