Of course, the word 'middle' was totally eluding me. And the example given above, I can assure you, comes from one of the verses quoted in Snorra Edda. If I could remember which poem I'd be even more impressed.
The Norse analogy came to mind because of the closeness of the sense of 'be bothered' to a reflexive. My terminology was heavily influenced by Latin (which is what I read nowadays). It would be fun if one had a spurious Norse analogy though - I wonder how one could construct a plausible(-ish) transmission for it?