To me, your best bet would be to bite the proverbial bullet and make the time to go to a women's "boutique" for brassieres. I think in this day and age, they won't be "put off" from the idea of helping a male person as they may have been in the past, and if you ask to talk to the owner/manager about any concerns you have might even score you an after-hours "personal" (aka shirtless) visit where their expertise (aka touching your bare chest) might really help you out?
I find it unlikely that you will find "your" solution via trial and error; you seem to be searching for compression type garments to solve it, but compression garments may not be what you necessarily need? To me, you are looking more for comfort and an ability to breathe normally while trying to hide your chest. There is no shortage of women that understand and accept that men might need help here, especially as we age.
Yeah, you might end up in a "lacey" or perhaps even "sexy" get-up if you go to women for help, and that might be hard to accept for a dude, but it is what it is. It's 2022, and yet society is still imperfect. To me, if a man is able to project comfort with himself, whatever that comfort happens to be, women will still latch onto that and find you attractive, if that is a concern.
Everyone has the right to be comfortable in their own skin. If your skin happens to have boobs included that "shouldn't be there", first off you are incorrect. Male boobs have been around since the dawn of history. We also apparently pioneered nail polish, earrings, leggings, high heels, and dresses? Gender Identity is provably bullshit when History is taken into account; we are all just "humans". We all have boobs, or we all eventually will.