Phonological inventory looks fine to me, don't you think though that all three of /b v w/ might be a bit much? Very few languages other than English have all three, and if our language is spoken, I'd assume most dialects would simplify to two or even just one forms ( just /β/ and /w/ for example).
Secondly, for the romanisation, why not take "x" for the sh-sound and "c" (or "ch") for the ch-sound? X for sh is common in many natural languages (Catalan, some South American Indian languages...), while I have never seen c for sh, tbh.
I actually think the "C" as sh and "TC" as ch makes sense... I also like having a letter for the hard h sound. But I agree that dialects would prove one of b, v, and w unnecessary. Which do y'all want to cut?
Alright. With "hard h" you mean the IPA [ x ], right?
If it were up to me, I'd keep [ b ] as is, spelled /b/ obv, and have [v] and [w] as allophones (or even just [v] and a labialisation of the preceeding/suceeding sound), depending on the environment - idk, have [v] in consonantic and [w] in vocalic environments, so for example /arva/ as [arwa] and /arevta/ as [arevta*], or whatever you prefer.
*or ideally [arevda] or [arefta], since differences in voicing between stops and fricatives mostly sound weird and are quite hard to do, imo, and get simplified very often.
