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Again, just posing the question sets off unconscious processes. I think the answer has pooped into my head! For the benefit of anyone else with the same question, here's what I think the answer is....
The aeolian can be converted to a harmonic min by sharpening the 7th note. If you do this for Dorian, Phrygian or Locrian (the other min modes) you don't get a harmonic min. In D Dorian, for example, to get D harmonic min, you have to sharpen the C (7th note) and also flatten the B (6th note). Here's the answer - you have D harmonic min but this is doesn't belong anywhere in C Major. The B flat is shows you that it's the relative minor of F Major. Same process for th eother min modes....