What's the next logical step in applying input to this FM transmitter circuit?
What's the next logical step in applying input to this FM transmitter
  circuit?


You've taken that step it seems. The audio mag field will wobble the emitter about a bit and you'll get a mix of AM and FM effects. The AM effects might not be pushing in the same direction as the FM effects and your receiver may not be amplitude limiting stuff as good as it should and along comes the distortion - a nasty interaction of half-limited AM stuff and proper FM. If you want a better transmitter try googling "simple transistor microphone FM transmitter" to get some images: -



After you've tried your hand at a few of them go stereo: -



Here's the website for the design and don't forget that all these transmitter circuits are likely to be quite illegal in most areas of the world.