I tried fixing this, but the changes I made didn't do anything (I saw no changes to the mesh in Nifskope), so I was obviously tweaking the wrong values. However, when I compared the old arrow.nif to the version from the UOP, I noted several changes. The most obvious and easiest to fix is the collision mesh on the quiver. The collision mesh on the middle arrow (I guess this is the arrow that gets cocked) was also changed. In both cases, the collision mesh was lengthened to encompass the arrows. I think the fix to stop the bowstring from passing through the arrow is to rotate the mesh on the single arrow component (cocked arrow) of the whole mesh. I tried rotating the mesh, but the values I was changing didn't have any effect.
In terms of making the quiver ride lower, I figured that this would be changed by changing the CofG (called center) of the quiver, but once again, when I changed these values, I didn't see any shift to the CofG.
I don't know anything about the UV mapping...
Would comparing the original nif to the one from the UOP help any? If your Nifskope skills are better than mine, then perhaps doing that would fix the issues. That's assuming that the problem is indeed a result of the version of Nifskope that the original UOP was saved as. If not, then you would be simply replicating the problem