When replacing the mattress, there are now mold resistant foams out there. I don't know the relative costs, but if the storage situation is likely going to remain similar, it might be worth looking into at least.

Of course, some people are allergic to the mold-resistant formula...

It might also be a good idea to get some sort of eggcrate foam layer or grooved ridged underlay for the mattress. Promote the circulation of air under it, and it's likelier to dry out and to stay mold free.

I watch too many home improvement shows.