Back when I first started writing, my eyes would quickly glaze over as screenwriting types would go on and on about three-act structure. I didn't care if it was Syd Field or Joseph Campbell or Linda Seger. It all boiled down to the same thing: answers that are too simple and too rigid. I don't take commandments well.
Only later did I come to realize the real power of three-act structure lies not in WHAT we write, but how we write... and in how readers and viewers receive your work. I believe that there is a sense of narrative hardwired into our brains, and it looks an awful lot like set up-conflict-resolution. You got it: three-act structure. It's in the way we tell stories. It's built into the language.
I'll probably always nod politely when a disciple of screenwriting guru X tells me that in this beat the protagonist absolutely must be separated from ally Y by the scheme of opponent Z because of his misbehavior blah blah blah. But I almost never write a scene or think through a beat without being conscious of my three-act structures. Yes, structures -- plural.
There's your overall structure -- the one you wrote up and reworked forty-two times in your synopsis before you even started to write the script. (You did that, right? Well done.) And then there's the three-act structure of the particular scene event. Finding a resonance between those two almost always helps me tell a better story. It's sometimes a tricky thing, and it does take practice. But it will help you find unity and reinforce your main conflict at every stage.
Why shouldn't it work? Think about it for a second. Let's get downright logical for a moment. Take a look at your climax. It should perfectly reflect the main conflict of the whole movie, right? It should absolutely resonate with your overall message. This means that your main character must be fighting the same internal and external battles on a grand scale. There's a set up, a conflict, and a resolution that feel almost pre-ordained by the rest of the script.
Now look at the inciting incident (the event at the beginning of the script that sets the action in motion). What is the hallmark of a good inciting incident? It plays out the same issues as the climax, just on a (usually) smaller scale. It tells the audience how to watch. It tells the audience how to watch. If it doesn't resonate with the climax, you're probably not satisfying the audience as much as you think you are.
Take any other major beat of the script -- the midpoint, the low point, inner cave, what have you. There's a set up, a conflict and a resolution to each of those. And you got it: each must resonate very strongly with both the overall three-act structure and the events that precede it. From a single idea you can generate huge amounts of story.
New writers often bristle at the importance of loglines and synopses. I certainly did. What I didn't understand is that a trained reader does more or less what I've done here. They take a few traits and a controlling idea (expressed in the logline) and they unfurl a huge story in their own heads. They look for story potential. They are often way ahead of new writers. Wanna catch up? Think through three-act structure from the ground up.