IMGTX:
Thank you for the picture as that is the same orientation that I found the black seal. I will be installing the grey seal tomorrow night.
Thanks everyone!

Any lip seal like in the drawing should be installed so that any internal pressure will push the seal tighter into the shaft it is sealing. If you install it backwards pressure will tend to force fluid past the seal, same with front or rear main seals.

I'll politely disagree and refer to the old saying "A picture is worth a thousand words"
Great job IMGTX

And to the OP,
1. Do not forget to check for lateral gouges or scratches in the housing where the seal sits
2. The bottom of the o-ring groove on the gear housing
3. The surface of the trans case that the outside O-ring seals against
4. Finally the shaft on the gear itself where the inside seal rides. EDIT: I just looked at your picture again. the area where the seal has been riding is visible. I would polish that area again in a circular pattern. HINT: A drill motor on the end on the gear works great
5. Push the seal in gently until it stops
6. Do the same with the retaining ring being careful not to compress the seal as it will deform it. (I normally use an appropriately sized 1/4 drive deep socket / nut driver etc.)

Minor issues can be polished with 600 grit or a fine scotch brite pad etc. If required it should be done in a circular fashion so any residual marks are circular like the seal.
Gouges need the be filled with something similar to JB weld and the leveled using the above procedure