You can't flip the third-member, period, it will rotate backwards if you do. You may be able to flip the housing upside down and put the third in it still upright, but then the knuckles are upside-down, and you have to put in new fill/drain plugs, and deal with getting oil out to the ends of the tubes.
The "reverse cut" gear scenario comes into play between low-pinion and high-pinion diffs.

Brent