Way back on page 35, but given linguistics is my specialty, I had to give some some late input/commentary.
The Inuit languages, at first glance anyway, seem to be a poor fit to a syllabic writing system, they have far too fluid vowels, too many diphthongs, and entirely too many consonant clusters. Looking a bit deeper, the vowels... aren't really all that important to a syllabary, if people pronounce them differently twenty miles away, so what? As long as they're pronouncing all of their vowels differently, it won't matter, and given that all the modern Inuit languages seem to have an underlying system of just three vowels, it's unlikely there'd be overlap.
The consonant clusters, in themselves, aren't an insurmountable problem, syllabaries the world over have come up with solutions, but when exposed to an alphabet, an alphabet is often what evolves, unless there is some critical cultural disconnect, or incompatibility. OTOH, humans seem to gravitate towards syllabic or systems like syllabaries, unless the language is incompatible, English being a notable example, allowing for truly horrendous consonant clusters, especially if compared to Japanese, whose syllable structure is (C)V(n). Incidentally, it turns out, in Kalaalisut at least, that the phonotactics are simpler than they first appear, most syllable-final consonants tend to merge and geminate the first sound of the next syllable, or otherwise assimilate to the following sound, I imagine the few exceptions are frequent, like Japanese /n/, languages tend to use rarer features more frequently if they have them, the English /đ/ and /θ/ sounds being extremely high frequency, and Indic languages highly prevalent retroflex consonants being key examples. Overall, it seems like a syllabary should work, despite my initial skepticism.