I'm probably overstepping my KSAs here; my experience with multicopters is limited to a couple of toy-style little quads. But it's been a couple of days.
As I understand them the controllers for multicopters take the rotational torque of the props into consideration, and in fact rely on it. That's one reason they require both CW and CCW rotations on alternate arms. So it probably isn't necessary to use contra-rotating props on each arm, and may in fact not work well (that's where I'm guessing.) Would love to see what you build.