“Let’s not forget that most of our saints are common to all authentic churches.”
I’m not sure how true that is. The RCC has a somewhat more elastic interpretation of the boundaries of the Church than we Orthodox or the Oriental Orthodox. Saints canonized by the Latin Church post 1054 are not generally commemorated in any of the Orthodox Churches. In the case of the non-Chalcedonians I believe that goes back even farther. Probably to at least the sixth century.
What’s “RCC”?
Yes, for purposes of things the Holy Church proposes for our salvation, it does not seem to matter in what local church a particular priest was active during his journey on earth. Of course, following the Great Schism, the knowledge of the lives of the split halves declined, and so did commonalities in veneration.