I think, actually, that particular 34D looks to fit you pretty well. But it's a strapless bra that you're wearing with the straps, so it's kind of a different animal. I don't actually se it cutting on you, but strapless are typically closed off on top so as to help hold things up without the straps. Are you saying this one feels like a turture device also?
Anyhow, as for the 32DD Felina, I think it's sitting too low on you. It's also possible that it measures small for a 32 band. Try measuring the stretched band and see if it comes out a 32". If it's not that or pretty close, it measures small for size.
T-shirt bras in this general style are a dime a dozen, and 32DD isn't particularly hard to find. You should be able to find lots of them. Try on others and see if they feel better in the band, while still fitting in the cups and giving you support. I don't think you'll need a 34 band once you find the right bra(s), because even though your snug and tight are close together, your snug is still an inch smaller than 32".
A few possibilities: Aerie Sunnie, Blakely, or Blakely longline (it's hard a longline bra; it only has two freaking hooks). The "regular" Blakely has a partial band like this Felina style you're trying and many, many others.The Sunnie and the Blakely longline have full bands, which might work better for you. Ditto the Wacoal La Femme #853117 and Parfait Jeanie. If you don't mind a higher gore, try the new Freya Idol, as Freya bras generally have have stretchy bands and are unlikely to feel too snug. Of course there's always the Freya Deco, which comes in umpteen iterations. And then there's VS--I think the Body by Victoria lightly lined, non-pushup ones are probably your best bet, but you're in their size range so go to town if you wish!