Well, even though I've got no experience on this whatsoever.... Here's my thought on it, though. Excessive moisture with a combination of a warm environment must be causing the mold, will they be allright without so much moisture? Is there a possibility you might be able to scoop some of the mold out?
You can use a product called "Tegosept" to prevent mold in your cultures, it's expensive but it works.
If you make cultures often go with the tegosept, if not do this; in a very clean mason jar or new 32oz deli cup mix 1/4 c potatoe flakes 1tbsp powdered milk 1tsp sugar, boil about a cup or two of distilled water for 5min, add 1/2 c of the water to the mix and stir it well, allow the mixture to cool to room temp. While you are waiting for the stuff to cool mix 10 grains of dry active yeast in 1tbsp warm water (115degF max 105degF min), when the culture mix is room temp add the yeast mixture. If you and everything you use is perfectly clean mold is not an issue. If mold is still an issue look at where you are keeping the culture.