Hi, Jill. I'm a little confused. Fabric softener sheets or a box or 2 of baking soda left inside the bureau with the drawers closed for about a week should take care of the odor equally between the drawers and the inside of the bureau. Apparently it did not. Is that right?
If this appears to be the case, I would apply a spit coat of shellac to the inside of the bureau unless there are obvious black patches of mildew present. If there are, take the piece outside on a nice warm day and wash the inside with a cup of household bleach to a gallon of water and a damp sponge. Don't use more bleach water than necessary and allow it to dry thoroughly. Then, apply the spit coat.
A spit coat is one part shellac to 5 parts denatured alcohol. Mix this in an old plastic container or an old coffee can and you can use just about any kind of cheap brush. Swab the spit coat on to all the inside surfaces of the bureau that you can get to. Be careful that you do not get any on the outside of the piece as it may harm the finish. Again, it's best to do this outside because the alcohol fumes can get to you. The spit coat will be dry in about 20 minutes and the odor will be sealed into the surface. Leave your container and brush outside and the alcohol will quickly evaporate from them too. When the old shellac gets sludgy, throw the container and brush away. It will not hurt the environment.
Good luck and let us know if we are reading your problem incorrectly. Henry in MI