I figure one of the pitfalls that initially led people to believe that this is gibberish is that they were looking at the language more as a substitution cipher (character to character) as opposed to a meaningful and completely separate language. Different languages have different grammar rules, and these can be found out from context. Here are a few examples of differing grammar from real-world languages, all relating to English so everyone here can understand.
Spanish: Adjectives are always placed directly after nouns. i.e. "girl pretty" vs something weird like "The girl is pretty" or "pretty girl"
Chinese: Possible to have outright tense-less verbs, 3 different forms of writing for the same spoken language
German: 3 different words for "the" (der, die, das, depending on the gender of the object), infinitive forms of verbs are 1 word and all have "n" or "en"
P.I.E.: 2 different words for different types of farts, unlike English (who says this inkling language would be all formal? Likely to not be so considering the old English dialect used in the readable in-game text, and the supposedly carefree nature of the inklings)
And, also, the biggest thing I must stress to the number movement: what are the odds the inklings would also develop a base-10 system? You did note a weird "11th" single-digit number, and this could be a sign that the base itself is different from the rest of the world. An example of a different base would be hex where you count to 100 like this: 1, 2, 3, 4, 5, 10, 11, 12, 13, 14, 15, 20, ext. Another example of a different base would be binary, which consists of 1's and 0's. 1, 10, 11, 100, 101, 110, 111, 1000. People working in numbers: I highly suggest you look into this base issue. While I did my research and inklings do have 10 fingers on each hand (allegedly meaning they are likely to come up with a similar base), who knows? Maybe 5 fingers on each hand led them to develop hex (not to be confused with hexadecimal).
Also, anyone thought of using the sunken scrolls to figure out some of this? Some of them to include inkling/octarian text, and the research notes appear to be a direct translation in some cases.