WI: Japan Invaded Korea...in the 1870s

Shortly after the beginning of the Meiji Restoration, Saigo Takamori, leader of the Imperial Army that ultimately deposed the Tokugawa Shogunate, advocated for an invasion of Korea. Although Takamori was utterly confident in the Japanese military's capabilities against the Koreans, the so-called Meiji oligarchs rejected the idea, fearing that they were still too underdeveloped to take on Korea and more than likely China. However, what if, for some reason or another, the Japanese government decided to initiate hostilities with Korea in the early 1870s?

Which occurred, unsurprisingly.
Ganghwa Island Incident

The problem wasn't going to war with Korea: it was going to war with China. Sure Japan could probably conquer Korea with some difficulties, but they were in no position to challenge China yet and everyone knew it. If the Oligarchs took leave of their senses, chances are we'd see a repeat of the last Japanese invasion of Korea: they'd get bogged down by Chinese and Korean troops and eventually forced to retreat to Japan.