Is it not just a problem with your inheritance of the ik's all of them are parented under another one.
I Took a quick look, I think, currently you only need to move the knuckle down if you want a press motion. I couldnt see any mesh errors in editor, and I don't have the time to test it in our implementation of C runtime (sorry)
The issue just looks the vertex ordering is messing up in the animation, and one face is over lapping the other? Try rearranging the vertex?