I'll start off by saying you're misremembering the 'battle' in GEN.I'm sure it's a feelings thing. I didn't think the "nooks and crannies" of the battle in Star Trek VI were well addressed. "How does Uhura (brilliant officer though she is) solve the problem of how to torpedo a cloaked ship when the best minds of the Federation could not?" "Why did this technology of firing when cloaked ever appear again?" Also, I think making a heat signature is a very 20th-century problem, isn't it? (This is the problem with not-military geniuses trying to write military geniuses. See also The Picard Maneuver.)
OTOH, I was fine with the battle in GEN. The rules were "The Klingons have sabotaged the Enterprise making her essentially defenseless until Data figures out how to turn the tables." Could they / should they have plugged some of the holes like "Hey at least shoot back" or "Show us why changing the shield modulation didn't work"? Sure. But after they teched the tech that would still have been the answer. (This is probably the same response I should have to TUC.)
It's Jack Dawson and the door. He could not get on the door with Rose. Because that's the story. If the prop maker made the door too big that doesn't mean Jack could have lived it means that the door needed to be smaller.
As for how a Bird of Prey could take out the Enterprise? That's explicit: They cheated. The Enterprise crew is even smug about how impregnable they are until it happens.
Why not just shoot a ship that's de-cloaking when it's shooting at you? That's been "hard to do" since Balance of Terror. Should it be? I don't know. It's a Star Trek rule. (In TUC they react like "can't fire when cloaked" is some physical law of cloaking tech. In Balance of Terror it was just an energy problem.) They take out the Klingons because Data figures outwhere the stock footage isI mean figures out how to get them to de-cloak when they aren't in a position to fire.
I was too busy wondering why the 50- and 60-year-olds were getting in a fistfight over a missile when they had time/space travel that would have made Time Lords jealous. Oh, and why didn't Kirk and Picard feel like they were wrapped in joy?
Also why nobody asked a shipload of refugees close to Earth WHY they were refugees? "Well, there was this thing called THE BORG..."
THESE are the things that bother me about GEN.
Data doesn't figure out how to penetrate the cloak, he figures out how to engage the cloak, which forces the BoP to divert energy from shields (or whatever). To that point the BoP isn't cloaked, which is why so many people find it so ludicrous that the E-D didn't simply blow them out of the stars once they opened fire, whether or not the E-D's shields were effective at the time.
Otherwise:
-I agree that it's odd that Uhura's the one who comes up with the idea in TUC.
-I think TUC itself establishes why this tech doesn't appear again, at least not that we've seen: because Our Heroes developed and successfully implemented a way to defeat it, and it didn't even take them very long to do so once confronted with the problem.
-Because the BoP in GEN isn't cloaked, and there's no immediate evidence suggesting the D's weapons grid is offline anytime soon, they're not even remotely defenseless.
-It's been my understanding that Klingon BoPs can't fire while cloaked for the same reasons that Romulan ships can't do it, which is a mix of not having the power to do so coupled with the reality that the power they'd need to be able to do it would render the cloak ineffective because they'd be emitting too much energy for the cloak to conceal.
Mostly unrelated:
-I always figured the El-Aurians were just very circumspect about why they were refugees. I'm not exactly sure why they'd be that way...but then, Guinan was always very mysterious in TNG, so it kind of fits.