You may need to have that much drop for solid waste, but I think almost any drop would do for water and nutrient solutions. You’re not putting in a toilet here! I would put the drain up against the back wall and have the rubber slope down to it. Then you hardly need any drop at all because the almost horizontal pipe is so short. You also don’t need a very big diameter for liquids. That’s why I suggested 1" PVC and 2 x 2s.
But what the heck, maybe you want a toilet in your grow room.