That still wouldn't make sense, since the exact same set-up was common in the Eastern Roman Empire, which had been thoroughly Christian for almost half a millennium by that point in time.

Honestly, it sounds a bit like a just-so story. Wikipedia indicates at https://en.wikipedia.org/wiki/Ad_orientem indicates that pre-Christian sects like the Essenes practised it, and that Origen (second & third centuries) & Clement of Alexandria (second century) both mention it.