I am actually about to do the exact same thing, using the exact same pan !
In my opinion, you DO need a pee-trap below the shower. I understand that stpace is limited in our under floor areas. But the purpose of the trap is to avoid odors from coming back up from the grey water tank.. And you and I both know they do have some odor. Especially after a few days in the heat..
My thinking is build the "room" for the shower and toilet from plywood, glue some FRP panels on 3 walls inside, then a curtain on the open end. I'm thinking about making the room another 2' longer, to allow a little "Dressing space" outside of the shower, a place to hang a towel, etc. With a 24' trailer, I've got the room I think. The width of these pan/tanks makes them have a small footprint overall.
Then just plumb my shower and kitchen sink drain to a grey holding tank, and there ya go !
Another option is to just run the grey water pipes to the dump valve, and carry a rolling porta tank with you. When you get to where you're going to set up, roll out your tank, roll it under the trailer, and put in your hose, and open valve.. Keeps you from having to mount any tanks under the trailer.