Funny, I have had the cup curling issue with a couple of bras. I am very much like you, in that not only do I like T shirt bras, but they have to be the smooth, silky material, as opposed to the more meshy, lace edged stuff. I cannot stand the feel, and they feel very tight, even in the correct size. I live close to a real lingerie store, and when I told the person there I couldn't stand the material on certain bras, she thought it was weird. She said the band should be tight... I hate that, because it itches me. I have found a couple of styles that meet my requirements, though.
I stopped buying bras on line 10 years ago, when this place opened up. I often joke with them, that I am the only suburban woman of a certain age that buys a certain brand of thong and bra, both of which they stopped selling. Last year, before my ski trip, I went in to buy a couple of more sexier type night-wear things. There was a new sales person, who was about my age (the owners are young) and she showed me stuff that looked worse than what my grandmother wore... however, I did find stuff I love. It's just funny that almost every brand of product I've bought and liked has been discontinued in the store.
2015 Trek Silque SSL
Specialized Oura
2011 Guru Praemio
Specialized Oura
2017 Specialized Ariel Sport