Having ditched the impossible-to-debug charlie-plexing idea, we've made up a board which simply places LEDs in columns and rows.
We're going to drive the "rows" through a shift-register (to allow more than 20mA current to be sourced) and sink them through a number of ULN2803A darlington arrays (since sinking directly to the microcontroller pin would only allow up to 20mA per row which could make a full row of lit-up LEDs appear quite dim).
Before we get clever with the sinking and sourcing, we needed to make sure that our array of LEDs worked - and to test it we simply connected the +ve and -ve terminals of a 3V coin-cell battery to the different lines on the PCB.
By touching the exposed wire ends to the positive and negative terminals of a 3V battery, we were able to confirm that every LED in the array worked individually of the others.
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