I believe ⌘F1 is used to activate “Display Mirroring”, which is a different feature than “Screen Mirroring”. The former mirrors the screen to an attached monitor, the latter mirrors the screen to an ATV or projector, for example.
It should be re-mappable via Keyboard Maestro, BetterTouchTool, or maybe even Karabiner Elements. But what do you mean it’s not quite working? Is it literally not working? Try fn ⌘ F1 instead of ⌘ F1.