I tried several approaches to get this to work, but the padding was the only solution which I could easily find. The disadvantage is that now an empty area will appear below the edit text, if the user scrolls all the way down in the inner scroll view. In my opinion, this minor inconvenience is outweighed by far by the advantage of being able to see what you type. :-)
Attached is also a screen shot of the way the screen now looks on my device. I tested this with several soft keyboards: the android stock, Swype, and SwiftKey.
Cheers.