Thanks for all the interesting replies! Given the response, I decided to make a whole community around this, hope you'll consider joining!
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If I love “unreliable shifting cities” narratives, like Dark City, Fallen London and the City of Saints and Madmen books, what similar kinds of settings might I like?
I'm not familiar with those, so this might be a bad suggestion, but the short description makes me think this may still fit, have you read The City & the City by China Miéville?
It's set in two overlapping cities, whose inhabitants diligently disregard the other city's until they formally cross the borders, and it's a crime to do otherwise. It's a pretty compelling read imo!
I haven’t but it sounds like I should. Thanks for the rec!
Kraken, also by Mièville, is also somewhat of a match; as well as Neverwhere by Neil Gaiman.
Maybe Palimpsest by Catherynne M. Valente? Her Orphan's Tales have some interesting cities too, but that's a bit of a stretch.
Again, not just one city, but take a look at Invisible Cities by Italo Calvino - it was a direct inspiration for Fallen London.
China Miéville might be worth checking out - go for either the City and the City or for Perdido Street Station.