Japanese Successfully Evacuate Korea After Invasion

It's been a while since I watched the Extra Credits video series on Admiral Yi, but ever since I watched it I had a question nagging at me and finally figured that I'd ask yinz your opinion.

After the death of Toyotomi Hideyoshi, the Japanese tried to negotiate a peaceful exit from Korea; the Koreans were not having it, and intercepted Japanese attempts to break their blockade at Noryang strait. The Koreans absolutely devastated the Japanese fleet as it tried to leave Korea, killing many of the Japanese invaders.

But suppose that a peaceful exit was successfully negotiated? Perhaps Admiral Yi was killed or incapacitated, or the Japanese managed to get the correct bribes to the correct officials, or perhaps some alt-history event pulls the attention of the Ming away from Korea and forces them to send their navy elsewhere, giving the Japanese more leeway to escape.

How does this change Japanese history, specifically the ascent of the Tokugawa shogunate? Does a larger surviving number of samurai veterans of the Korean invasion tip the scales against Tokugawa, as they fight to protect the power of the Toyotomi family under the regency of Ishida Mitsunari? Or would these veterans turn against the Toyotomis and/or Ishida Mitsunari, either siding with Tokugawa or trying to take power for themselves?
 
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