So the following is I'm an Old Chick...yet I'm learning a new trick...experience.
I have sloped shoulders. My bra straps have fallen off of my shoulders on a daily basis since I started wearing one at age 12. So much so, that I don't even think about it any more as I reach inside my shirt to grab my bra strap and put it back into place while talking to family, friends and even total strangers. It's weird.
So, I finally gave up at finding a bra that doesn't do this... I have searched for 40 years... and succumbed to a cross back bra. It was hard. It totally bugged me the first, second and even the tenth time I put it on. It was a struggle to pull it over my head, t-shirt style and blindly do up the hooks with my hands behind my back, but I survived and I'm happy to report that you will no longer see me reaching inside my shirt anymore at random-awkward times to fix myself.
This is an Old chick learning new tricks. It can be done.