Sorry, I hope this doesn't count as "necroing" but there are 2 options I think people are overlooking:
1)
Jeju uprising of 1948 grows into a fully-fledged secessionist revolution and the creation of a "Jeju Korean Republic" or something. The uprising would likely need a foreign backer for that to happen.
2) The
Koryo-saram are given their own Korean Autonomous Oblast within the U.S.S.R. (probably somewhere in Central Asia or maybe even on the
Sakhalin Islands — lol, can you imagine how pissed Japan would get??

). Once U.S.S.R. dissolved the Korean Oblast is upgraded to an independent republic.
Both PODs don't
strictly fulfill the OP since ronaldo specified the "Third Korea" should be located between North and South Korea, but hey, since others brought up things like Yanbian Korean Autonomous Prefecture I thought these options should be worth mentioning.