16 loads, eh? That's a lot of washing! Glad you are getting through it. Would you consider getting tanking in your basement (its a moisture proof membrane inside the walls and floor)
I am sorry to say that, if the walls are prone to seepage, I would not store fabric there, even in plastic containers- the air will be damp and that will get into it one way or another, unless you have mechanical ventilation or a dehumidifier going.