I'm late to the thread.
I had an apartment once in the basement of a house that had terrible humidity. I bought a room dehumidifier and ran it day and night. (You know, the kind with a tank you have to empty.) You should do the same thing for the bedroom in which the firearms are stored. Keep the door closed, so you're only dehumidifying the room. You won't believe how much water gets sucked out.
My basement in my house is really dry, but I still run a dehumidifier in the summer.