No I think it's Remake!Aerith - Rebirth - CoLW!Aerith (dream world edition, dies there in the LS) - Rebirth (dies there in our world) - Remake (resolution, she does go back in time aware that his or maybe her feelings are an illusion) - Part 3 (Lifestream edition) - ACC.
I don't think OG!Aerith especially exists, she is just Remake Aerith, an expanded version of OG!Aerith. But CoLW exists after the Remake trilogy too. The insertion of CoLW Aerith exists because Aerith needs to question her own feelings for Cloud, to not get stuck. The church there was her Promised Land and that's why she ultimately met Cloud there, because it was her wish, but she realised her error. This is why the church where Zack landed is Rebirth!Aerith's Promised Land, because it will be her wish to meet Zack there, I think, and as a Cetra, it will become reality.
In short the end of p2 exists for CA to get their ending, and for Aerith to be able to transition back to Zack, most probably. Without it, we see her circling around Cloud (CoLW), but Nojima clearly wants to detach that Aerith, that used to be closer from her OG self, to the one we see at the end of ACC (yes, you're supposed to draw romance from ZA there and it's a clash with CoLW so it has to be explained).
So our Aerith does a nearly whole round before ACC before getting killed by Sephiroth, but outwits him as she sent herself back in the Lifestream "earlier" than her own death, which means that by dying... Aerith comes back into the Lifestream.
I'm not sure I'm clear but it does make sense in my head.