some thoughts to start
The East had a India / China dualism whereas European culture rested solely on the Greco-Roman World. Although Rome = China is suggested often, I'd rather have them be India because of the heterogeneous nature of the ancient Mediterranean. The Roman Empire can fall apart sooner and basically be like Ashoka's India, known for the patronage of a culture / religion than lasting political rule. Or Maybe a more widespread Hellenic Empire that includes Rome and falls apart as usual, never to recover. What would the Roman equivalent of Buddhism be? Neoplatonism, maybe?
The Celtic World can be China. A unified Celtic empire around the same time as Rome that somehow keeps the Germans confined and becomes more of a trading partner to the various post-Roman states. We can have a Celtic Confucius that provides a philosophy similar to that of OTL China, while Neoplatonism makes inroads. There is no exclusive monotheism and more or less a philosophical system imposed upon existing polytheisms rather than a clean break.
The Germanic tribes can be like Manchus and Koreans, pushed and confined to Scandinavia and often at odds with the Celtic Empire but just as often its tributary states. And yes, Britain makes sense as European Japan for all the usual reasons.
The Slavs would be the Mongol Analogue. On the periphery of civilization and always invading left and right while retaining their pagan religion until the late middle ages.
Maybe we can have a Tibet Analogue in Dacia, with its own idiosyncratic priesthood inspired by the Cult of Zalmoxis, and Theocratic rule.
Maybe for the East, We need more unity between India and China... maybe have India stay Buddhist, with Buddhism solidifying around a couple of pope like figures in Indosphere and Sinic World each. So the difference between India and China is more like Rome and Byzantium, made even greater by the fact that India is always invaded by people from beyond the Hindu Kush and relies on Chinese mercenaries to fend them off.
As for China's dissolution, we can have a very intense invasion of China Proper by Barbarians at the same time the Chinese are having dynastic crises, famine, etc. Maybe all due to meteors striking Central Asia or Something. They basically start outnumbering the dwindling Chinese in their many Kingdoms, and the only vestige of the former Chinese Empire is the Great Temple, home of the Great Buddhist Priest, who becomes a pope analogue.
The two problems here are making a homogenous Celtic Empire and making Buddhism have a Pope-like figure. How Plausible is this? Any more ideas?