We've traveled for 9 years, fulltime, never, ever had a problem with things stored in the basement. Moldy = moisture in the bays = water leaks. First should be to figure out how you're getting moisture built up in the bays. Since we are into a bay every day or two, there is always fresh air moving around. I store out-of-season clothes in vacumn bags and then place into a long plastic tub on rollers so it is easy to move around. Might it be that you are smelling adhesives that off gas from the luggage? We also don't carry that much in the way of 'off season' clothes - - we follow the 75° mark and add/take off as appropriate so we really wear the same clothes year round. Especially this winter - maybe 3 weeks total without shorts on.
Barb