First of all, I am so sorry that this podcast is ending. It's been a fun ride.
I'm old enough to have watched this episode when it premiered. (I was 11) I don't know how to explain how different the attitude about America was before the 70s, and especially before Watergate, but seriously - we saw ourselves as the good guys in every story. I think anyone watching this would have been Team Kirk all the way. That made an ending where the Federation were not morally superior hit harder, I think.
Re the racial coding: I think they did what was easy. It made the Klingons visually distinct, although in my memory they were more generically "not white people" than Chinese. Also, in my memory the Klingons read as unambiguously Russian.
Given that we were living in the era of The Truman Doctrine at the time, less formally known as "Containment", Kor's rant did not read Japanese at all. We were literally constraining Communist regimes. However, Kirk's comments about invading our territory could be read as talking about the Japanese, especially if one were thinking about the Philippines rather than Pearl Harbor.