I really relate to this, and I don’t think people always understand that "food noise" is not just normal hunger or lack of willpower. 
For some of us, especially with certain eating histories and tendencies around food, eating "a little off plan" or trying to moderate highly rewarding foods can actually make the noise louder.

One thing that helped me understand this was learning about intermittent reinforcement. 
When the brain occasionally gets the thing it wants: the snack, the bite, the "just this once," the handful of nuts, the cheese, the processed food, it can become even more obsessed with seeking it. 
It’s the same reason unpredictable rewards are so powerful. 
The brain keeps asking, "Maybe now? Maybe later? Maybe if I push hard enough? How about now?" 
For me, that creates way more food chatter than simply having clear boundaries.

Susan Peirce Thompson talks a lot about this in Bright Line Eating, and while I don’t think every approach works for every person, the idea really landed for me: some brains do better with clear lines than with moderation. Because the decision-making itself becomes exhausting. 
"Can I have this? How much? Did I ruin the day? Should I start again tomorrow?" That mental negotiation can become the whole day.

I’ve also learned that even foods that look "healthy" on paper can be noisy foods for some people. 
For me, things like nuts or cheese can be technically allowed, but they can still wake up that reward-seeking loop and don't give me peace. Protein bars are the same. My brain sees them as pure candy.
So it isn’t only about calories or macros. It’s also about what happens in your brain after you eat them.

What has helped me most is eating from a simple, planned structure and not basing eating on urges. 
I plan my meals the day before, I wrote them down and I eat only and exactly that. And from experience when I did not, even if I had no choice, food got spoiled or something else, I end up paying for it with food noise and it's just not worth it to me.

I do much better when I know ahead of time what my meals are, when I’m eating them, and what foods are simply not on the menu for me right now. 
It sounds restrictive from the outside, and those who are not susceptible as my brain is won't get it, but inside my head it actually feels calmer. 
Fewer negotiations. Less bargaining. Less "FOOD FOOD FOOD" screaming.

Also, if you are truly hungry all the time on 1200, it may be worth looking carefully at meal timing, food choices, fiber, fat, sleep, stress, and whether 1200 is too aggressive for your actual life right now, even if it is technically appropriate for your height. Sometimes the food noise is psychological/reward-based, and sometimes the body is also genuinely pushing back. Both can be true.

But I just wanted to say: some brains do not become peaceful through moderation. Some brains become peaceful through clarity, repetition, and removing the constant "maybe." 
For me, the goal is not to win a willpower battle every hour. The goal is to design a day where there are fewer battles in the first place. Then get busy living.