O.K., so you:

1) dissassembled the diff and inspected the gears inside.
2) Checked the outdrive splines/key for damage (with both outdrives in the diff, hold one and the diff body, and spin the other. It should not be able to spin at all).
3) Checked the front bevel gear on the driveshaft for damage/missing pin/key (see that it is not spinning freely on the shaft).

By the pics, your outdrives look fine, so the only places that could be producing the problem are the ones noted above. You missed something. If you didn't disassemble the diff, you need to check all the internals again. I'm thinking now, that a pin/key is broken or missing in the diff somewhere.

It's definitely in one of the three areas. Check it again.