I just saw a video of someone doing braiding using a Japanese stool like device (marudai) and also a braiding disk (kumihimo), both reminded me of dodecahedrons (the mysterious Roman gadget described in the linked video).
What if the knobs weren‘t there to hold the string but rather to simply keep the braiding strands separated from each other like with those braiding devices? Using it for braiding would also allow to produce braids of different thicknesses, thus the different sizes of the holes would make more sense and it doesn’t matter that the individual devices are of slightly different sizes. Now the question would be why soldiers would need so many braided strings.