In reply to clochette:
I know you'd like something more gentle, but regular household bleach in dilute solution is probably your best bet. It' not so unhealthy, you can use it to purify water for drinking after all (the dose makes the poison). You want to kill the mould, so anything you use will be at least a bit hostile to life if it's going to work!
After that, pay attention to prevention: remove water whenever required with squeegee and lots of ventilation!