Very interesting, but I have great doubts on how a fallen mandate can be kept by a ruined dynasty - was the exile-Ming really stable?
Once the guy is out of China, you have to stop thinking in Chinese terms like that.
When the guy is in Okinawa, he's just like the forgettable Ming heirs in Taiwan - irrelevant, practically speaking, yet still a threat to mainland pretenders. He doesn't need to keep the mandate to be a threat - Koxinga had the mandate by no stretch of the imagination. He just needs to be there.
And neither is the fallen mandate relevant to internal Japanese politics. The Japanese attitudes towards dynastic rule were based on permanence, not on a cycle replacing the decadent with moral warlords and peasant rebellions. If a Tang heir married into the Fujiwara, the contemporary ruling class (for all intents and purposes), Japanese concepts of succession and legitimacy would obviously take precedence.
This isn't actually a Chinese dynasty running in Japan. This is a Japanese dynasty with an unusual and interesting progenitor, and a foreign flavor. However to the Japanese, it is
felt to be a Chinese dynasty, so for those purposes it is so. And to the Chinese, it is felt to potential threat (because duh, it is), regardless of the fact that the dynasty will soon be 1/8 or 1/16 Chinese (and possibly unable to speak any form of Chinese fluently). Chinese dynasties didn't rely on the loss of the Mandate of Heaven to protect them from past dynasties. Despite the simplistic formula that suggests those dynasties would simply cease to matter, they usually took care to wipe out, cloister, or otherwise eliminate all potential heirs to their predecessors.
So, judging by the way the Japanese managed heritable rank in this period - the relevant metric - the purported "Tang exilic dynasty" could be expected to be stable indeed.... in the admittedly long-shot circumstances I described.
Furthermore a ship in China can reach Japan within a month or two, so Japan has no reason to believe in the glory of the Tang dynasty when they hear of their exile in Okinawa.
Nothing in the scenario I described required Japan to not know that the Tang have fallen. The Japanese delay in lowering their estimation of China was not due to not knowing the Tang had fallen on hard times (and then ceased to be). The continuing high estimation of China by Japan was a result of the contemporary culture having built up Tang China as an ideal. The culture's first response was not contempt of Chinese weakness, but horror at the destruction of what they still considered the greatest state and society. So there is every reason to believe that the Tang dynasty brand would have a certain cachet in the period's Sinophile Japan.
Look at the history. The Tang were overthrown in 907 - but already in 923 there was a Tang restoration attempt. That lasted 13 years, despite not having much basis to speak of.
This is the period in which a plausible Tang pretender arrives at the Japanese royal court. If the Tang name had sway in Mandate-of-Heaven China sixteen years after utter collapse even when promoted by generals who in fact had little to do with the Tang.... Then why should the Japanese, with their much more immutable ideas about royalty, not see significance in a member of the Tang line of succession?
Furthermore, dynasties don't hold much significance themselves IMO - the Ming-in-Taiwan was only possible because of the enormous fleet it held. If any dynasty or ideology held great significance then the successors of Confucius should have more prominence in Chinese history, but they barely did. Institutions by themselves don't hold much significance, especially devoid of power.
This seems... a bit off.
Dynasties don't hold much significance? Chinese dynasties for two millennia were obsessive about removing or managing anyone related to the preceding dynasties. Not that it's peculiarly Chinese; it's fundamental to dynastic politics in monarchies.
"If any dynasty or ideology held great significance then the successors of Confucius should have more prominence in Chinese history, but they barely did." Uhm? I'm not sure where to start.... Before the comma is you make a questionable assertion offering no evidence, and after the comma a claim that is directly contradicted by every take on Chinese history I've ever heard of. The successors of Confucius were
barely prominent in Chinese history...? Their words were still the root of legal decisions affecting millions
in the 20th century, for heaven's sake!
And the "institution devoid of power" that we're talking about is the Imperial dynasty of Japan. The one that played a significant role in world affairs a thousand years later.
I'm sorry, but you've really lost me. Could you be a little more clear, or something? I didn't propose a very likely scenario - and certainly not the most likely outcome of the first POD - but your commentary seems off base.