What happens after 5. Nd2, 6. d3, and fianchettoing the king's bishop? White seems to be just up a pawn with a safe king, good central control, and lots of ways to play.
When I was trying to do the exact same thing you're doing (coming up with things to do with the Nimzovich that didn't happen with other openings) a few years ago, the best I could come up with for 2. Nc3 was 2. ... e6, followed by d5, though that can also be gotten through the French...
I was recently shuffling pieces around on a pocket set and came across something interesting. I was trying to find advantages achieved through the Nimzovich Defense (1. e4 Nc6) that are not transpositions into other defenses. I found this line to be the most compelling. It arose from White converting to the Vienna Game (1. e4 2. Nc3), an opening I despise playing against as Black.
Here is my line: 1. e4 Nc6 2. Nc3 d5?!
White's most accurate continuation is Nxd5, leading to a "permanent" sacrifice, a sacrifice in which material re-compensation is not forced.