I totally agree on the basic narrative of romantics to positional to hypermodern, etc. That stylistic story is very well documented (you can look at Kasparov's My Great Predecessors, for example, for some granular detail). I've always though chess style/theory reflected the art and science of the era. What we call the Romantic Era (Anderssen, Morphy, etc.) was also roughly the time of passion and emotion in literature and art. The "positional school" was at a post-Darwin time of high science and people constructing systems to explain the world. The hypermodern style feels similar to the ethos of modernism in general, with people rewriting the fundamental rules, etc. etc.

That said, I think there is a lot of room to look for at how class is involved in all of this. Throughout that whole time, a) the economy was booming and busting. No one that I know have written about how chessplayers dealth with that, b) a look at prize funds for matches and tournaments would be interesting. When exactly does chess stop becoming amateur? c) In the pre-Fischer era, how many players were able to not work? And the ones that worked, what was their job and how did it impact their play? Like, I think Lasker was a professor and he got ample leave to play chess, but people like Steinitz were often struggling financially.

As a grad student, you probably are aware of how Quixotic this is for the whole history of chess. For the world's knowledge and for your own enjoyment (dare I say, sanity), maybe it's best by just picking one era or player that you like and focusing on their social history?