Removing the clearcoat is the messy part. Food coloring stain can be drawn to the surface with a damp towel first. An oxidizer will then eliminate the color. I have not used a bleach solution, but Oxi clean works in dillution as well as lab cleansers. Aniline dye, which is very hazardous, is colorfast when lightstruck and is what many gibsons are colored with. It is added to the lacquer as opposed to staining first. Try the coloring on scrap, and then try removing it.
It has worked for me on a variety of stringed instruments that used a water based dye.
I would just live with it on a box though.
Craig