Mozilla should develop a rudimentary Blink or Webkit mode for FF that allows it to fallback to a better supported engine (with obvious limitations wrt extensions, privacy policy) for select websites. I think once the user has opened Chrome/Safari because something rendered all fucked up in FF, they're likely to keep using it. The telemetry from fallbacks could be used to prioritize compatibility issues and drive down the number of sites that require it. Oh and replace its own netstack with something better like the one from chrome.
I’m not sure if the specifics but I think embedding an alternative rendering engine within a browser already built around a different one would be a significant chunk of work.
I could imagine a sort of quirks mode though, just a few hand selected chrome bugs/features implemented in gecko to make it behave just a little more like chrome. What a horrible future but it’s a possibility.