How to perform a block-wise frequency down-shift?
As an aside, are there other caveats I should be aware when performing
  a down-shift, that I haven't accounted for here?


Yes there's one and let me put one of the most important caveats when performing frequency modifications. An acoustic sound signal (in the form of a music, speech etc) will physically exist in a so called harmonic structure (for more indepth discussions see sound synthesis, sound analysis etc.) whose immediate implication is that the perception of the frequency content is in octaves rather than linear frequency decades (an octave is the span of frequencies between $f_0$ and $2 f_0$).

Now, eventhough for most technical applications (such as in those communication algorithms) a band of frequencies can be shifted to any desired frequency without a loss of information (which forms the essence of the modulation theory) when it comes to audio perception this does not hold.

It's easy to see that the harmonic structure of the audio band will be distorted when a complete band is shifted to other frequencies in a linear manner. As a solid example consider a primitive audio waveform composed of $440$ Hz, $880$ Hz and $1320$ Hz (these are $f_0$, $2f_0$ and $3f_0$ of an absurd instrument, more natural instruments will have more complicated structures including inharmonicities etc.)

Now if you linearly shift this waveform base from $f_0$ to $1.5 f_0$ then the new frequency distribution will be $1.5f_0$ , $2.5f_0$ and $3.5f_0$ which are no more harmonics. This creates an important problem in natural pitch shifting applications.