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?
