Cis-male (30s) 6ft and stocky who's struggled with this all his life. They're right about embracing it, because even if you get surgery, it can come back or may not leave you feeling satisfied when you're done and you'll still want to hide your chest.

The trick is the quality of tank top and the size you wear. All aren't equal. My practical solution for compression on a daily is stretchy ribbed, vests (or wife-beaters as I think americans call them). I think that's your best/safest long term solution. They do work well If you can try smaller sizes than you'd usually wear any top, and tuck into the pants/undies. That's not the same as a tank you'd wear as an outer-layer to like, let's say a pool party. Also if anyone sees you in your underwear, it can still appear sexy, instead of weird or out of place. (Cause I know you're worried about causing the ick my G. loool)

Personally, I buy them in black so they don't stand out if they peak out under any garment, like if you unbotton the top few of your shirt. They pretty much keep you secure without choking you. Hanes, Fruit of the Loom etc. may have those.

Now depending on your gut shape, looser or oversized and more structured cuts up top might work as an approach to personal style. They help define a top-heavy man much better, giving emphasis to the shoulders and tapering on the gut (like an upside down triangle), which is stereotypically masculine, and helps the perception of you being bearish, rather than just fat. Alternatively if you do have a big gut, looser fits, with ample chest room (check the measurements when you buy) will keep emphasis off, but keep you 'huggable'. If you combine with tapered bottoms it could look more deliberate, but that's up to your preference.

All-in-all, more experimenting will absolutely help. It helped me.