Okay, First of all I do not know what I'm talking about. That's my disclaimer right up front!
Now, have you considered a tea bath for the whole project? I don't think it'd alter the darker colors but it would tone down the white. I have never worked with tea but have seen the results and they are lovely. Several ladies have used the tea bath to dye fabrics. Put it out there and see what they think. It'd sure be faster than a ton of applique.
Of course, I think it's just lovely the way it is but I like white with most anything. That's just my quirk!