[Guy]

Well there you go ! They did use a cookie cutter approach for the basics back in the day. That pvc stack is a clone to the one in our coach, so fo the most part, you do have factory plumbing . As to the thought of trying to drain sink and shower water into the black tank by reversing the two dump valve positions, I don't think we should try to fill a black tank from the bottom. Being old school, this black tank has a toilet sitting on top of it, so we know what is in the bottom of that black tank.

Your descriptions of pipe functions make me think you have a streetside kitchen? Ours is drivers side, so that is a plumbing difference. That blanked off left pipe was for a drivers side kitchen sink .  I would think that the center pipe was meant to drain in  the top of the tank, but the left pipe could be redirected to do do.  With the 4 gallon per minute water pumps, Newell did not see a need to vent the drain stack . The waste tank is vented by what we would consider to be an "oops" overflow pipe coming from the top of the tank and out thru the  bottom of the water bay
Now we just have to figure a way to terminate that left pipe into the top of the tank.  I want to believe that you could cut out a hole in the top of the tank and insert a male pvc adapter since it is gravity application. 
If this system has been hacked by a prior owner, there might be a blanked off hole on the top of the waste tank?

Now, isn't this easier than electrical ?