Connect shower to existing grey water drain

I currently have a septic system just used for grey water and currently only has my washing machine is connected to it. The washing machine is on the main floor and all I see is a vertical 2" drain going into the basement and directly through the basement floor.This setup currently works fine. I would like to attach a bathtub to this same grey water drain but it is 25 feet away. The bathtub currently uses a 1-1/2 inch drain and has a P trap and vent and works fine currently. I am wondering why I can't just run the existing bathroom drain 25 ft by dumping the 1-1/2 inch pipe from the bathtub into a 2 inch pipe and tie it into the existing vertical grey water drain using a wye or sweep. I would plan to have the 1/4 inch drop per foot .

Will this work OK?

I don't see why not if it's a legal setic tank.
Just make sure, that you keep the current vent for the tub.

So running the horizontal 25 feet will not be an issue then? I was thinking after reading some threads that anything longer than 10 feet would maybe need additional venting as the drain would be potentially blocked with water while draining due to the overall slope.

Also where my 2 inch drain connects to my vertical drain should it be a wye fitting? What if I I want to incorporate a clean out where or near where this connection is made?