Here is a video I watched, for anyone in the future who has this issue, that helped me:
I tried three times with my duck on her back and each time it was so hard to feel what was happening as I pushed the prolapse back in, and it kept popping right back out. I just tried again with her right side up and I was actually able to feel much better when it was fully pushed in, and it stayed! I know this victory might be short-lived, but we are calling it a night and going to bed and all is well for the moment. After it stayed in she practically flew out of my arms into the bathtub and had a nice long bath, and is now in her dog crate standing in her water dish. I'm sure she's not happy to be away from her friends and stuck indoors, but it will be good to keep an eye on her and keep her clean, and she's overall pretty calm.