That was also an observation I made but found after reading up on the extra data block that it isn't necessary, and provides additional physics info for the mesh.
The good news however is that I have made progress I think! It appears Oblivion doesn't like it when a material doesn't have a name, whereas Fallout doesn't care (and in this case it bit me in the butt, because all of the materials were un-named). I don't know if this is actually documented anywhere, so I'm going to make a mention of it to the Niftools guys to see if they could implement a method of giving un-named materials a generic name on export for Oblivion settings.
What I'm still trying to figure out is why this didn't work when I tried it last night (6 hours of troubleshooting earlier). The possibilities are that I either missed a material or that I had to, for whatever reason, use the Update Tangent Spaces spell after renaming the material (which is what I did this time). Now that I have a good lead on the problem I'm going to take a break and try to get the full mesh working later (I stripped it down to just one NiTriStrips to test on).
EDIT: So, after getting the full mesh working, I noticed that it seems every object in the mesh is using one normal map. Is this a limitation of Oblivion? To allow only one normal map per mesh? Here's a picture -- defects are apparent on the grip and cylinder: