While I'm going to acknowledge beforehand that this suggestion is unlikely (not unlike the whole premise though, really), its just something I'm throwing out there.
Historically, the Ming attempted to get Toyotomi Hideyoshi to halt his campaigns in Korea by placating him with the title of King of Japan. Toyotomi historically declined this, ostensibly because he felt it would be disrespectful to the Emperor, to whom he still owed at least theoretical, if not actual, fealty. Obviously one can assume that other factors featured in his decision besides respect for the Emperor, but it would not be prudent to simply dismiss this as an important factor. In any case, however, I am digressing...
Perhaps one could make an argument for Toyotomi Hideyoshi accepting this title from the Ming court. He had often felt scorned by his title of Regent, which he saw (rather correctly) as a consolation prize for being denied the title of Shogun, owing to the common knowledge of his low birth. Had he accepted his Ming title, it is theoretically possible for the Ming to make political inroads into his court, perhaps in the form of brides, consorts, or concubines. In such a scenario it is rather more likely that each dynasty will endure past its historical end-point, as one of the major contributing factors in the final decline of the Ming was their being forced to exhaust the imperial treasury funding Korean resistance to Toyotomi's continuing invasions, and a strengthening of Toyotomi's dynasty with Chinese ties could cause a different result at the Battle of Sekigehara, or perhaps even preclude Tokugawa Ieyasu's coup entirely. With such inroads in place, and increased longevity for each respective dynasty, it is possible that the Chinese and Japanese courts will become more close, perhaps even to the point of joining somehow. In this way it would be theoretically possible to achieve a Ming Japan.
As I said before, this isnt a 'particularly' likely scenario, but its the best and possibly most-creative-while-still-remaining-grounded I can give you.