Agreed. I've always liked FASA's notion, which might have also been suggested by other contemporary sources, that there were worlds within Federation boundaries that were either not full members (associate members, with fewer privileges and responsibilities) or non-member worlds that, in some cases, had been incorporated to shield them from the influence of the Klingons or Orions. Not all of them were necessarily primitive compared to the movie-era Federation, but they weren't necessarily interested in official membership at that point either.
It's been a while since I've seen the ep myself, but IIRC the problem was that the Fed/Cardassian war caused problems on a number of border worlds, and the two governments eventually agreed to swap some of them to help create peace. So the Native American group might have originally settled on an undisputed Federation world, but wound up being forced to leave it to the Cardassians or submit to their government, which they ultimately did.
Perhaps you'd be willing to agree to disagree on this point, because while I understand some of your points, I also agree (with no disrespect intended) that you're reading details that aren't necessarily there. I've never interpreted the situation in TUC to be one where the Klingons were literally on the verge of extinction, nor do I think they would have been entirely unwilling or unable to solve the problem so that Qo'Nos is still habitable (or if that fails, so that some other imperial world can become the new capital). Certainly it makes sense that neither party was comfortable with a "new era" of cooperation, but I'm willing to bet the Feds made at least some inroads before the TNG era. Otherwise, the TNG Empire wouldn't be a major power on par with the Feds, Romulans, or others, and wouldn't be as willing to allied with the Federation.
It depends on how the war is being fought by both sides, and we don't know most of those details. Alt-Yar says that by 2366, more than half of the Starfleet has been lost to the Klingons and Picard says that defeat is now considered inevitable within six months, though the Feds obviously don't want it public yet. I think therefore the Klingons managed to win some strategic victories that ultimately made them more likely to win, and Riker says there have been significant Starfleet victories as well (Archer IV in this timeline).
We also don't know to what extent "neutral" powers might have had an influence, like the Romulans. We saw in "Redemption" that Sela's forces were supplying the Duras faction with supplies crucial to their victory, and with which they might have won had not the Feds cut off the supply line. That sort of politics can play a huge role, as we also saw with the Dominion War (Sisko had to pull out all the stops to get the Romulans on the allied side, since they had signed a non-aggression pact with the Dominion). The Cardassian government under Dukat allied with the Dominion, and later switched sides at Damar's urging when they realized that their alliance was no longer on an "equal" basis.
I'd say, for the reasons I mention above, there are more than just these two possibilities. Evenly matched powers, and even very strong empires, can spend a long time fighting if they're not stupid enough to waste their resources carelessly and they have enough leadership to provide at least some victories, perhaps even strategic or decisive ones. Napoleon, like many other conquerors, might have suffered from no small amount of hubris after he became emperor, but it's fair to say he also earned his place as a great warrior. Had he made different choices and not overextended himself in Russia, things might have turned out much differently for Europe.
I'm becoming tempted to move this thread into GTD, since it seems more of the discussion has to do with the political aspects of the PD and not the technological aspects that might play into them. I know it's a difficult element to separate, especially when the canon sources have fudged the PD so often.
