For the second case, is there an argument that this process was unambiguous and objective in terms of a fairly wide range of metrics over color spaces?

I don't actually have much idea of how far, numerically, colors vary due to different illumination, or due to different digitization processes.

In this case, the Piet palette uses about 8 different colors and 3 different "steps" of luminance, so it seems hard to mess it up too much even if it's based more on a human understanding of colors then a mathematic one (orange -> orange, light blue -> light blue, dark blue -> dark blue, white -> white, etc).

It's also interesting to note that, for Piet, the colors themselves don't have any particular meaning, the instructions are encoded by the differentials between one color and the "next" color in the program direction, with blocks of continuous colors encoding noops. So moving from red to light red is a [0,-1] change, (no hue, 1 step lightness), and moving from blue to dark red is a change of [4,1] (4 steps of hue, 1 step of darkness). So the exact colors don't matter too much