New build - quad or tri?

Hi All - we’re developing an unusal flying object and I’d like to see if anyone can give me any compelling reasons to go one way or another regarding quantity of directional thrusters. The basic flight frame consiss of 2 centeral, co-axial, vertically oriented contra-rotating impellers for generating all of the downward thrust. Yaw will be controlled/compensated by varying the torque of one or both motors. Pitch and roll will be controlled by either 3 or 4 bleed valves (located evenly around the circumference) that divert small amounts of thrust air at a greater distance fromt the center than the primary thrust, thus creating a moment to counteract any roll or pitching tendency (or control commands).
This could be thought of very loosely in principle (from a control point of view) as either a tricopter or quadcopter, though what would traditionally be propellers providing downward lifting+controll thrust are simply actuators providing control thrust. Of course the theoretical minimum to define a stable plane is 3 points, but four (e.g. quadcopters) control points have become much more commonly adopted. Wondering if there is anything inherently Arducopter specific that would lend itself better to the physics involved with 3 or with 4 control points. Thanks for any recommendations or pointers with regard to Arducopter and tri vs quad control.