Atlantis had existed as a mythological concept for way longer than Cthulhu. Adding fictional civilizations based on stuff made up thousands of years ago feels less forced than ones based on stuff made up a century ago. Once you add Cthulhu worshippers, people would start asking to implement more crossovers with popculture, like Warhammer factions.
Maybe instead of a full-on Crusader larp which would feel like a weird match with Eldritch horrors, something like “Occultists” based on the theme of secret societies from Templars to Freemasons pulling the strings? Ideally they’d cover more than just Chthulhu pandering, I imagine each major god would cover a different occultist theme: one for pacts with the Devil, one for the starry wisdom of night sky (Cthulhu goes here), one for Enochian/angelic magic.
I imagine you could even throw hot air balloons in.