To tone down the brightness of yellow paint without making it darker, you would add its compliment, or purple. Try this: Put you quilt on a neutral surface (a beige sheet is good) and lay your purple fabric along two sides to see how that would look as the major part of the border. Maybe a narrow inner border in the pink or blue, a wider outer border in the purple, and binding in the blue or pink. I think you'll find the yellow will fade back since it is the only color from that side of the color wheel.
Also, part of the reason the yellow stands out so much now is because that is what is framing the whole thing. Once the border is on, any border, the yellow will not be the focus!
I wouldn't undo anything you've already done. It truly is lovely and your friend must have special reasons for wanting those colors for this memorial quilt. Best of luck.