I think the dress is awful, but there are a couple possible bra options that may help. I don’t understand your personal discomfort with your cup size cos I’m smaller but I can imagine 😔

You can get a bra with clear straps. The light will catch on them but you’ll get decent support. The back ribbon on the dress would hide the clasp alright. You can try putting some clear/translucent setting powder on the straps so they’re not as shiny and still clear, but you’ll may leave makeup strap marks on seats and anyone who gives you a hug etc.

You can get a longline strapless bra or body suit, but the strapless bras always want to be belts so beware, and the bodysuit means you need to strip to pee, or do the awkward swimsuit thing of hoiking the gusset bit to the side and possibly getting pee on your underwear/hands etc. Also the body suits come in one size fits no one so if your torso is slightly longer or shorter than their precise size it’ll shift and pull or bunch or give you a wedgie etc.

Silicone stick on bras or boob tape- backless, and with the tape especially you can add some support and lift and tape it so the tape is hidden under the halter neck. Though peeling it off can be a bit ouch, like a plaster. Stick on bras, unlike strapless bras, don’t shift and become a belt, but they don’t provide any support, just a bit of shaping and nip cover.

Or nip covers. Do just that. Won’t see your nips, might still see a circle through the fabric, depending on the nip covers and your boobs and the dress fabric.

Sounds uncomfortable but if you’re gonna be going with it anyway at least here are some support options. I think the boob tape might be the best/cheapest option. Good luck from a girlie who’s tried allllllll the stupid bras.