WI: Yi survives Noryang and coups the Joseon?

From what I have read, Yi was not the kind of person who would do such a thing, and he seemed to be loyal to the state despite the several times when they absolutely fucked him over. He was basically the Belisarius of Korea, if we can make that kind of comparison. So a change to his disposition, while not affecting his military career and subsequent rise, would make him not loathe or averse to the idea, and is it at all plausible that, perhaps sensing imminent execution by Seonjo and the same corrupt officials and generals who led Korea to such disaster in the Imijin War, attempts a military coup, in the same vein of General Yi-Seong-Gye, also known as king Taejo, almost 200 years earlier, killing Seonjo and using his son Gwanghaegun as a puppet, eventually disposing of him when he is no longer needed? I am not sure on Yi's administrative abilities, but his actions on the Manchurian frontier suggest that he was capable in non-military matters as well. How would said dynasty engage with the Jurchens? It would probably be quite weak in the beginning, but if he can score quick victories in Manchuria without weakening his state, could that allow his regime to survive? How does this alter the chaos the Ming experienced in their later years? And would he be able to manage Korea's recovery from the Imijin War?
 
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