Carl, this was a thoughtful, exciting and well written piece. I really enjoyed your thesis. However, I strongly disagree. I say this amicably, because there are many interpretations of Wittgenstein, and they have respectable arguments in their support.
Imho... Wittgenstein did not deny personal internal cognition, emotion, feelings, etc. The ideas you referenced were about how people talk about internal states. It's the "talk" part that only has meaning in a social environment.
Perhaps the crucial point here is we use language internally. It's language that's shaped by society. It's only in that way that our inner worlds are shaped by society.
This dovetails with Wittgenstein's private language idea -- your inner states defy meaningful description in words. If you call an inner state "pain" you don't know if other people would call that "pain." Wittgenstein is not denying your feeling, he is saying it's meaningless to use a social construct to name (to define) an inner state.
More broadly, Wittgenstein said (at the famous end of the Tractatus) that anything that can be said in words can be said clearly, that if it cannot be said clearly in words, then it is beyond words, other than poetry or the like. In this light, Whereof we cannot speak, thereof let us be silent" is both practical wisdom and poetry at the same time.
My reading of and about Wittgenstein is listed in my Medium article "20 Years of Schoolin' and They Put You on the Day Shift."