What meditation practice(s) are encompassed by 'asubha' (non-beautiful)?
The core buddhism's meditation is not about body parts or anything related to outer world. It's always about the dependent co-arising. 

Below is about the uninstructed run-of-the-mill person from Assutava Sutta


  "Monks, an uninstructed run-of-the-mill person might grow disenchanted
  with this body composed of the four great elements, might grow
  dispassionate toward it, might gain release from it. Why is that?
  Because the growth &amp; decline, the taking up &amp; putting down of this
  body composed of the four great elements are apparent. Thus the
  uninstructed run-of-the-mill person might grow disenchanted, might
  grow dispassionate, might gain release there.


And below is about instructed disciple of the noble ones from same Assutava Sutta


  "The instructed disciple of the noble ones, [however,] attends
  carefully &amp; appropriately right there at the dependent co-arising:


Therefore based on above, the famous asubha meditation conflicts with that sutta. So the reason should be asubha is misinterpreted. 
Explained detailed on Asubha meditation is in Kuddaka Nikaya-1 -&gt; Asubhanupassi Sutta (If anyone found an english reference please add). This says that sabba sankharesu aniccanupassino viharathi That's the abstracted meaning of asubha meditation. (I'm referring to sinhala - pali cannon, sorry I can't translate this to english)

There's another sutta which clearly says that, Noble meditation should not be based on air, fire, water etc. I'll try to find the reference to that as well.

With this you might be confused by now. Yes, most of the meanings are mis-interpreted. The real dhamma is out there now, It will come famous but will take sometime to accept by people.

With Metta...!