Okay, so I'm back to report on the swimsuit idea. Apologies for the quality of the pictures, but getting a shot of your chest when you can't see what you're doing is no easy task. Hopefully it won't be too hard to tell what the effects of each one are.
Yes, I have pictures! Two comparisons each; on its own, and under a loose Tshirt. Apart from the first two:


This is just to show what I have to work with. In that shot I'm wearing a sports bra, and I'd not long finished working out - because I do that at home, I'm less bothered how I look.
Anyway, onto the first swimsuit idea I had:


This is a one-piece swimsuit I bought years ago, back when I wasn't thinking of binding. High lycra content and does a.. not bad job, although I sweated buckets the first and only time I went outside in it.
Onto my current binder:


This is the top half of a two-piece swimsuit I bought on ebay - this time I did buy for binding, so I bought a size too small. I have mixed feelings about it if I'm honest - does about the same as the orange one in those pics, although I've since got a slightly better result with it. Still, it's not too bad under that shirt, so it's good for the time being at least

Oh, and the best part? It doesn't make me sweat, and is generally more comfortable.