Just when you think you are getting things figured out, you realize that you really don't know much at all!
Here's what I was right about: the wet bath really does have a waterless p-trap in the floor. And it really is working in reverse since the interior diaphram is inside-out.
However, I was wrong about what caused the backflow issue. I learned I was wrong because, well, it happened again!
I had assumed that the washing machine caused the tank to overflow, but it turns out that it was my kitchen sink...which actually makes more sense.
I am now certain that my kitchen sink drains into the back holding tank (along with the sink from that bathroom), and the washing machine drains into the front holding tank (along with the shower and upstairs bathroom sink). How do I know this? Because I forced two of my children to watch the hoses outside as I ran the water in the camper and to yell out when they saw water running through the hoses. Mystery solved!
So why did I think it was the washing machine? Because it was my first time doing laundry when the tank overflowed. However, I was also washing dishes at the same time, which I had done many times before.
But the second time it overflowed, I was washing clothes with that hose open... yet the tank overflowed again! Ah, but I was also washing dishes!
Are you following all this?
Anyway, after cleaning up yet another stinky, nasty, gross mess in the boys' bathroom, I think we've solved the problem:
1. Know what drains into which tank.
2. Leave the grey water tanks open most of the time.
3. Spend 73¢ on an air-tight plug for the floor drain so you don't have to deal with the stench wafting up the pipe!