The PICO-8 actually has 32 colors from which we can choose any 16. I understand that making use of the default palette is the article's intent; I'm just thinking aloud.

If one were wanting to render an image on the PICO-8 itself, the ideal algorithm would select the best 16 colors from the full 32-color palette which, when dithered, produce the most perceptually accurate version of the original image in 128x128 pixels. Were I a smarter man I would create this, but alas.

I think this is how the original Myst image compression worked. Every image used an 8-bit palette, but each palette was custom for each image.