If you can't eliminate the water running through the root cellar then your options are limited. One option is to paint the exposed wood with a biocide laced paint. Places like Home Depot sell the biocide additives and then will mix it in for you. You would have to wait until the affected areas are reasonable dry to paint or else it will just bubble off. I know some of the restoration companies have industrial size dehumidifiers that will dry out the cellars
Be careful of the industrial ozone generators. They will kill all the mold spores in the area. They work with high concentrations of ozone which can be deadly. Smaller units do not produce enough of a ozone concentration to kill mold.