I think it's better to come up with replacements for those Google services and apps instead of rewriting the entire operating system. You need to solve the same

I think it's better to come up with replacements for those Google services and apps instead of rewriting the entire operating system. You need to solve the same problems on a linux smartphone as well, so Android gave you a lot of time savings, and I doubt the app sandboxing is even remotely as good on those non-Android linuxes. For Google Play for example there is F-droid, for push messages/FCM there is UnifiedPush, for Google Maps there is Osmand.