Joy & Vix -- I wish with all my heart I could do those things. I'm VERY busty, with a small band size for my weight (despite being borderline-plus sized, my band size is 34).
The local Nordstrom does not carry any bras that fit me. There's a specialty shop about an hour away that might, but I mostly order bras from the UK and Poland to get a good fit. I could call that shop about their strapless selection and see how it goes, though! Worth a try.
My other option, which I've used in the past for bra-unfriendly stuff, is some kind of cover-up. I have a black cashmere bolero....... hm.