In the case of Omega Glory, Miri, or Bread and Circuses for that matter, it is assumed these are cases of Hodgkin's Law of Parallel
But there is also the Preservers to be considered, namely in The Paradise Syndrome. What if instead of parallel versions of Earth, that these were actually planets where seeded by the Preservers using humans they gathered from Earth during various eras, as well? If that is the case, then these are basically lost human civilizations. And if that is the case, does the Prime Directive really apply, in the first place?
Now Captain Tracy was clearly in the wrong no matter what the situation was. So regardless if the Prime Directive applies or not, Kirk was essentially repairing what damage was created by Tracy, as best as he could. SO if the PD did apply, he didn't violate it.
I can see lots of dissent over what the document is supposed to mean after Kirk and party depart. Note that when the original American Constitution was drafted slavery was in effect in the U.S. Certainly looks like the founding fathers weren't including those enslaved as being equal with everyone else. Extrapolating from that I imagine there would be lots of Yangs insisting their holiest of holies can't possibly apply to the Comms as it does to them.
Well, if the preservers WERE involved, then I would say that the Kohms and the Yangs were plucked from Earth during the Cold War. If that were the case, then the Yangs' constitution must have included the 13th amendment.