I've had the v2 for a few months now, and it's been fine until today, possibly because I didn't notice it before since I have always had the restrictor ring - I almost always have the analog stick mapped to keyboard keys.
But today, I wanted to use it as an analog stick, so took off the ring and quickly felt a resistance like the one described by the OP.
It's a hard resistance that happens only when moving the stick in a general back/up direction. It occurs near the center, as you first start to move the stick. Move it a bit further, and, it suddenly breaks through whatever is causing the resistance. At that point, you can continue to move the stick back/up out to its limits, and the resistance is the expected minimal resistance, where really only the centering force of the "pull back" spring (or whatever provides the centering force) is felt.
Per this thread, I tried turning the stick clockwise. Going to the limit (fully screwing in the stick), the problem is worse than if it's not fully screwed in. Unscrewing the stick in a counterclockwise motion until the globe starts to hit the outer edges of the ring of course causes lots of resistance in all directions of stick movement.
Somewhere in the middle is best - it's there that I can find a spot where the resistance to back/up motion is better, though still not absent, and difficult to deal with.
Aside from the resistance to back/up motion still being there, though, the problem is that with the stick not fully screwed in, the screw can freely rotate in and out as the stick is used, which quickly moves it away from the spot where the problem is least noticeable.
Anything else I can try for this? Thanks!