After having a similar experience with the same yarn: Sugar n Cream but in a different color, I switched to a laundry detergent also which preserves colors: Cheer. Jeans also don’t fade out, none of my wash gets that washed out look like it did before and it is clean. I also use Borax when I wash, dissolve a 1/2 in some water and then add it to the wash load. Borax gets whites whiter and doesn’t let colors soak into other items as much. It also boosts the detergent’s effectiveness as well as being antifungal and antibacterial which is why I started using it years ago for doing diapers. It gets rid of mildew odor also.
Of course the damage when I discovered the ombre yarn faded into the white yarn was done, but since my project was a rug for my bathroom, it was not as big a disaster as yours.
I suggest that you make several swatches and soak one in vinegar and another in salt and then also get the Cheer detergent. I have one of those front loading machines so I have to use the liquid. And you will know what works then and then you save your formula and will know what method of washing will work.
Johnson and Johnson, “Shout Color Catcher”, another product which is designed to fix the color to the fabric is reputed to work fantastic. If it isn’t carried in your local store, you could order it on line. I’ve heard it works like a charm but have not tried it personally.
I’ve also read that the Hobby Lobby’s cotton yarn is colorfast, but I have not purchased it myself. I do not live near a Hobby Lobby so much for that, the brand on the website to look for is “I Love This Cotton Yarn”. They also sell yarn dies, I’ve noted, so a project which faded might be able to be fixed up to look acceptable, though I’ve not dabbled with this. Sometimes a great technique is developed because of one of life’s many disasters, as mother of invention is alas, necessity.