I used to be a project manager for a demolition and abatement company. One of the things we would do is mold and fungal remediation. Obviously you don't want to introduce any hazardous chemicals to this environment. Borax is a fairly benign mineral, it is also a fungistat - meaning it slows the growth of fungus, mold, and mildew. After you clean up the floors with peroxide it might be worth wiping the surface with a borax solution. It's dirt cheap and people use it as a laundry additive. At your local grocery store or Walmart you'll find it either in the laundry or cleaner aisle.
I keep a box handy for cleaning up around the house. It doesn't produce any fumes or have a substantial scent.
It won't kill mold, but in my experience is does slow down mold growth in humid environments.
BORAX very Good Stuff, I have it around just like a bottle of DAWN, and of Course what life would be like without a Can of WD40 a must!
Between those three you can clean just about anything!
I have used borax before, it does work great. I should keep a box on hand next time I do a tent cleaning, using two methods would probably help a lot.