The section on the Braavosi language is really interesting and deserves to have a wider audience. It really shows how commited this community is. Maybe reference could be made to it in books in chests, or signs on inns or ships? I think it would be really cool to have a few easter eggs relating to it.
Also, on the subject of language, does it really make sense to have all of Westeros speaking the Common Tongue? Maybe a Song of Ice and Fire is actually translating what is a very wide array of different dialects which may not even be fully mutually intelligible, like Arabic? There is a vast amount of potential for this: we could be mapping out movements of people, relations to older languages, development of architectural styles based on different groups of people, the gradual mixing of Andal and First Men languages and traditions... This has so much potential.
Also, on the subject of language, does it really make sense to have all of Westeros speaking the Common Tongue? Maybe a Song of Ice and Fire is actually translating what is a very wide array of different dialects which may not even be fully mutually intelligible, like Arabic?
It seems like despite it being a little bit unrealistic, the whole of Westeros speaks the same language and someone form the North would be able to understant someone from Dorne without problem, so the degree of dyglossia is not as high as in Arabic.
"Yes, Westeros has regional accents. I played with the idea of trying to depict them with phonetic misspellings (and indeed I do a little of that, with some less educated characters), but that way lies madness. I try to suggest the accents with syntax and taglines instead."
George R. R. Martin
Creating a world with few languages is useful when you want your characters to be able to interact without problems and focus on their dialogues, relationships and power dinamics. Adding a severe language barrier would make it harder.
That being said, there are quite a few references to accents and speech patterns that respond both to place of origin and social class, so there's room to explore. At the end of the day it doesn't really matter, since making a map of dialects and making a map of accents, for example, deploys a very similar result. Defnitely something with room to work with, I fully support your proposal!
My sense is that "Common Tongue" is just a fancy way of saying "English" that doesn't require England to exist. And just like English, the Common Tongue would be largely intelligible across dialects with the existence of regionalisms and primarily phonetic differences. However, there very possibly also could be unintelligible dialects, especially in the more isolated regions.
Also, fun fact: David J. Peterson, the creator of Dothraki and the Valyrian variants, is at least somewhat aware of my version of Braavosi (which I based on his work), since I presented a WIP version to him back in 2015 when he gave a lecture in my Invented Languages course in college!