Not sure if this solution is applicable as I first read about it when a chef wanted to make his uniform as white as possible.
Find a way to put juice from lemons in the wash. That's how he did it, but read up. I also read he used actual lemons instead of lemon juice. Your materials may be too different from his for this solution to be effective.
His whites were what car dealers call "super white".
The problem with white cars is that they only look their whitest in the showroom.