I made all 7 duplicates in the same way ... made a material for each, unwrapped each, and OF COURSE one of them is somehow rotated :|

oh.

there's gotta be some wonky thing where the cursor or something affects the way the uv unwraps for a selected face

It’s just making sure you are paying attention

Oh it's such fun isn't it? I especially love it when the collada exporter changes from using "materials" to using "textures" and merges all my faces into one because they all use the same texture in blender!