Many trailers have the black tank installed above the subfloor, with the toilet mounted on top. I understand that the strategy is so the trailer can be used in freezing conditions, and the black water is kept warm by the interior of the trailer. In cold temperatures, the grey water system, since it might be below the floor, is either not used, or is used with all valves open so that it is continuously draining, not storing water that will freeze and burst something.
Your grey water tanks need to be below tht level of the floor in order for your shower to drain into them. Your black tank needs only be lower than the toilet. You will want your black tank to drain straight out the bottom, for best empty-ability. If you did use a VTS tank that is level with the belly pan, your valve assembly is going to hang way down.
It is hard for me to imagine you getting all the black crud out of a VTS tank as well, considering the high ratio of bottom surface area to side surface, and considering the bottoms are flat.