I totally get it, but hope you also see the logical conflict.
I dunno... Getting creative... I suppose you could compensate via your own button? A "done" button on your layout that manually closes the keyboard (easy to do... search for this), and the button becomes visible while the text field receives focus (events for this). I suspect the trick is to delay making it invisible after text field has lost focus for at least a brief moment, because it looses focus when you click your done button.
Also - Having users hit the back button to close up the keyboard should NOT be unnatural to your Android users.
There may be some hints to take away from a general Android search, such as
THIS