Began by getting as close as I could with selections from the 56-hue palette (the colors on the far left, excluding jet). Then figured out how those needed to change to match my ideal version of the Art Deco palette (the next column, indicated by the black triangle). Navy was complicated because I have rules about how modifications to BaseHues can't stack too much ink in one place, or get too dark—i.e., in CMYK, C+M+(Y/2)+(K×1.5) can't exceed 180. So the K formula for that color ends up being (180-((C+M+(Y/2))/1.5.
I treat teal as the index color from which all others (except jet) are calculated. So the red-orange slot, for example, is always the index BaseHue minus 24 (and wrapping around to 56 if less than 1). Confusingly (to me), in Excel, the actual formula for that (since there's no 0 BaseHue) ends up being MOD(IndexColor-25,56)+1. Then the result gets its CMY values multiplied by 0.95.
The next four columns are the subpalettes generated from different index colors (7, 34, 41, 55).
The process of figuring out how to translate an existing palette to my own grammar was engaging. Think I'll try this again with a different palette.