I've gotten to Kingsparrow with low chaos. Has the game stopped caring about chaos at this point, or will going on a murder spree tip the scale and wreck my ending?
No, going on a murder spree at this point will no longer affect the game.
Whatever happens in the mission is determined prior to loading the level (this is why the maps are also identified by the chaos level associated). The ending cutscene, then, is determined by the choices made in the final mission - therefore also unaffected by your changed chaos level.