The Portuguese and Jesuits really missed a bet in Korea, which was not xenophobic prior to Hideyoshi's invasion. The Koreans believe in a one god named Hanumim. Buddhism had to make a great many adjustments to accommodate that belief. Christian missionaries were unexpectedly successful when they came to Korea in the 19th Century. They would likely be unexpectedly successful in the 16th Century too. Portugal might be able to use this success to make inroads into Korea and maybe even conquer it from within. In all likelihood, the Portuguese could at least manage a closer trade relationship than they had with China and Japan in Korea. At least until Hideyoshi comes in, and probably thereafter if they give Korea military aid.
And from Korea, perhaps Christianize the Jurched-Manchus before they even think of conquering China.
Korea is another place where Spanish silver (as well as Hawaiian and New Guinean sandalwood) may open many doors. Especially if Spain can get in before the Japanese invade Korea. Because when the Japanese do invade Korea, the Koreans will want Spanish guns and maybe even military advisors. And be willing to tolerate Christian missionaries in the Korean countryside to get both.
And if Koreans become as enthusiastic about Christianity in the 16th and 17th Century ITTL as they are in the 19th IOTL due to their belief in their one god Hanumim, Spain may have the fifth column within Korea that it needs to actually take over the place by say, 1650 should the Yi attempt to crack down on Christianity. Not to mention be given some new ideas on naval tactics such as low to the water iron clad "turtle ships" from Korean Admiral Yi Song ye that may have unpredictable butterflies in Europe.