Someone has to shed light on the 800-pound gorilla in the room: I like Victoria's Secret. They have a lot to choose from, with tons of support down to very little, and all sorts of materials in use. (You can also get a matching thong to go with it!)

Another place you might look is in the swimming suit separates at someplace like Academy. Perhaps a light-weight swim top would be more comfortable than the fully-constructed bras you've been finding. They also have a variety of band or tube-type tops. Even a snug tank top might offer some of the type of support you want.

SRS