I found myself in a similar situation, and I feel like I'm just finding my workable solutions!
I am large-chested (38 DDD), and no matter how much I bind, there will always be something to notice until top surgery. So I am figuring out how to balance the desire for a flat-appearing chest and what my body can physically handle. Mentally, this is tough, and continues to take daily (almost minute-by-minute) practice. I remind myself that some men have more prominent breast tissue. I also look at myself in the mirror to show myself that I am WAY more flat than I give myself credit for being when I am looking straight down at it.
I am never going to pass, even with binders that would prevent me from breathing or moving. Tough to accept, but it's my reality. But my friends and coworkers are using my chosen pronoun, even with the obvious chest. The people who matter see me for who I am. I just have to remind myself that the opinions from the strangers on the street doesn't in/validate my transition or who I am. Their confusion is their own.
Then, there's the physical. After much trial and error, I've found a binder that works well when I add a thin-fabric crop-top underneath (which provides traction for my skin so they don't migrate to the center as quickly). The key for me is being able to truly, fully breathe with the binder. I got several panic attacks when I tried on my first few binders, and I realized it was because of the specific location of my lower ribs it was crushing. If I am struggling to breathe, I can't think about anything other than my chest. I was also hurting my back and shoulders with my previous binders, so I was beginning to be in daily pain. But now, with the right binder set-up, I can actually go 30-60 minutes without thinking about my binder!
Long story short: don't give up on the binder search! I had given up hope of ever finding a comfortable, non-harmful method until just a few weeks ago. I spent a lot of money, time, and pain with binders that didn't work, but I am thankful I kept looking and was able to find something to make this last year of binding a bit less tortuous!