If I'd like to give the user fine and coarse control over input gain, is that something that can be handled with the way the recorder works in Superpowered?

Yes, using Superpowered you can fine control input gain. Check the frequency domain Android project, throw out all code not related to audio I/O, then use the primitive functions in SuperpoweredSimple.h to change volume, then use the SuperpoweredRecorder to record the incoming sound to disk.