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Last time I ran mine my deer was covered in green growth by the time we got back on the weekend... I'll run a dehumidifier next time I do it. Ours is 6 inch walls, concrete floor with drain, R38 wall insulation IIRC, and OSB inside painted to be sealed and the 10x10 is WELL sealed.
If this is only on the surface it can be removed with white vinegar and usually the meat is fine. Don't know if there is any truth to this but have heard white or green fungus/mold is not harmful but black colored ones can be, an actual growth not the usual discoloration of drying.. If it is below the surface and into the meat then it can only be cut off to salvage the meat. If there is a strong odor I give up, mild odor I will cook a test piece to see if it is salvageable. The French and other lovers of "high game" age their meat to this point intentionally.
It also sounds like your storage unit needs either some ventilation or combo dehumidifier air conditioner.
