I would adapt the lens you're viewing this through.
Going muscle by muscle, while it has merit, is much harder than viewing the movement you're trying to correct. You're already seeing that with your valid Good Morning question.
Extending your example, say Good Mornings do work the hamstrings more than the lower back. They might be worthwhile for you then, no? However, what if you're doing your Good Mornings with too much lower back arching?
The above is how a client of mine was hip hinging before he met me. (It's fairly common due to many over worrying about not letting their lower back round / flex.) It doesn't matter if that hinge worked is hamstrings more than his lower back. When you're engaging in a habit, you sure aren't going to get less likely to do that habit! In order to help his excessive lordosis we merely stopped hip hinging that way.
Another example. Leg Raises strengthen the abdominals, right?
However, Leg Raises also work the hip flexors. Oh, and what if you're doing your Leg Raises while allowing lordosis to occur? Like this?
You're going to run into these questions a lot. You mention stretching the hip flexors, but if you stretch them with a big lower back arch, that is again reinforcing the movement you're trying to avoid:
Instead, you'd want to think about "How can I not move my lower back into too much extension?" Then apply that to whatever movements you're doing, possibly in conjunction with the muscle approach. For instance, here are a couple ways to stretch the hip flexors while being more mindful of not moving the lower back-
Credit and credit (<- this link is a full guide towards getting out of APT).
If you feel you have too much lower back arch during the day, then merely pull your stomach in a little bit. You typically don't need months of strengthening and stretching to accomplish this. It's not like the pull of your lower back is so much stronger than your abdominals, that you aren't capable of generating some posterior tilt until you spend a couple months strengthening the abdominals.
An under appreciated movement is overhead lifting. Do you arch your back when you overhead press?
You'd want to correct that too. (More details why this can happen with overhead lifting.)
Bench pressing and it's common to have a big lower back arch. There's another time you might want to flatten the lower back (though this can lessen how much weight you can lift).
Pull-ups and you don't want this going on,
(Tips on how to correct chin-ups.)
Again, examining the muscles has merit. I gave some links with more details showing how that lens can be beneficial, but unless you have a solid anatomy background, I find my clients have a very hard time grasping all the nuances of that approach. I'm happy to educate them some, but much like getting your car fixed, I don't expect to be able to solidly learn how a car works just because I stop by the mechanic a couple times. It is much, much easier when I tell them, "Hey, just stop arching your back, during everything." The muscles usually take care of themselves (though, again, I still will implement some dedicated work in that way).
Plus, stretching and strengthening is no guarantee of anything. After all, if you sit for 12 hours a day, but you do a few exercises a few times per week, that might not be enough volume to offset all the hours of sitting. Yet changing how your lower back moves is guaranteed to...change how your lower back moves.