Yesterday's Enterprise isn't so much of a problem, since much of the "facts" gleaned from that episode take the form of speculation by a bunch of war-torn officers from a parallel universe. And yes, I know it supposed to be an alternate history based on our own but that really doesn't work logically, since the key event (a big explosion at Narendra) is a natural event in the timeline without any external interference. As a result, the outcome of the Ent-C's adventures started and ended 20 years before Picard finds the anomaly, with an alternate timeline not even on the cards.The Redemption War in TNG could be reinterpreted in that context, where the Klingon military isn't actually that large and most of the combatants were really just private militias whose allegiance to the Empire was theoretical at best. That would, however, require quite a bit of tinkering with the internal logic of "Redemption" and "Yesterday's Enterprise."
The only other reference to the Ent-C and Narendra is in Redemption during Selar's introduction. But then it is merely referred to as an "incident", with no mention of alternate timelines or Klingon armadas fighting the Federation. So in the Prime timeline we really don't know what happened at Narendra.
Together with interpreting the battles in Redemption as the result of private militias, the events of TUC seem ever more plausible in a TNG set up.
You're kind of throwing "Yesterday's Enterprise" under a bus with this explanation, but there are no obvious problems. Hell, for all we know the lack of Data's head in San Francisco is what triggered the War timeline in the first place
