I'd advise against the black grease. Treat the thrust washer the same as the main spur gear - very small amount of silicon grease on each ball and them assemble the diff.

The grease is only to help the balls roll in the cage. Black grease is to lubricate under high loads. That last thing you need is to lubricate the balls in the thrust washers - we want them to grip, not slide.

Yes, you may well get better performance from the diff is you use the washers the other way round. This build will give you more point load on the balls making it grip more with less end load. Also, there will be no friction between the balls and sides of the grooves as they rotate.

Providing the washers are hardened on both sides (they should be) this is worth a try to see if you get a better diff action. HTH