After opting to use Surface Shaders instead of mia_material_x Shaders, it was pretty apparent that, whilst the flat colour looked good, it still needed something to break the colour up a bit.
After my previous tests, I'd decided that I wasn't too keen on how traditional texturing looked in this instance. Instead, I've tried texturing in After Effects instead, using overlays of various textures to give the impression that the animation is actually a moving painting on a flat plane.
In Fahima's painting, the image is made up of several different materials, so I've attempted to emulate this diversity of materials in this test. To achieve this, I rendered out masks for each colour and then used each mask to isolate a unique texture. These were then used as overlays on the original video and the end result was the video above.
I really like the unique outcome of this combination of fixed textures and 3D models. I need to balance out the textures a bit, as some are a bit more jarring than others, however this is a pleasant outcome regardless. I am considering animating the textures somewhat too, just to break things up a little bit more.
Update: In response to Phil's comment, I have attempted to make the textures less static by animating them on twos.
I think this does a good job of keeping all the motion uniform, but I will still need to find a away of balancing out the textures in the final animation.