Fellow small-band, large cup ladies, I sing unto you the gospel of Freya (also, Fantasie, Cleo by Panache, and Elomi, among others, but Freya was my first discovery and still is a favorite). Before finding Freya at a local independent lingerie shop, I was entirely unconvinced that the center panel REALLY ever sat against your chest, that anyone made anything over a D cup in a non-minimizing style and/or a fabric that could be described in any way other than "utilitarian", and that I would ever join the ranks of "cute" bra wearers. Freya altered my existence. Yes,they are expensive, but once you know your correct size, and if you are not picky about being "on trend" you can find last season's styles for half off or more on a variety of websites, including eBay (new with tags, not used) and retailers like Nordstrom Rack.
Join me, my sisters, in the land of the properly supported, non-minimizing and non-exposed in v necks. There is joy here.
Also, I recommend Old Navy for shelf-bra-less tanks and Lily Padz for "headlights"