Anti-rust barbicide could be something worth exploring. I looked around the forum and found a guy with my exact same problem AND the same model of Dovo. The picture he posted nearly matched my issues here, a few "spots" of light brown, it was mostly attributed to hard water stains in his case (I wish I remembered the forum link!). He said he used CLR on it and it cleared it up.
Since I've been drying it thoroughly and storing it in the bedroom rather than the bathroom, there's been no new rust or stains.