My initial thoughts and research  on how to create the software side of this project has brought me to Fluidsynth.

Fluidsynth is a fantastic bit of software with many features, but one feature is exactly what I need; it capable of generating notes from MIDI data using a loaded soundfont. With some work this could carry out exactly what I need the Pi to be doing in this project.

Fluidsynth has no GUI and is operated via command-line. It has a python module on Github too. This is fantastic - I will be able to write my own python scripts and control it exactly the way I like.

The Arduino could even just pass simple commands rather than MIDI data and have the Pi then generate the midi to pass to fluidsynth. 

Hurrah!