The cleaner came yesterday and sanitized the basement from floor to windows with steam and microbicide.  Then he brought in a small army of dehumidifiers and fans -- enough to make the electric meter spin faster than I'd ever seen it -- and in a matter of hours the humidity was down to 50% again, where our own dehumidifier could take over.  Now the basement smells fresh and clean.  We have to resist the urge to put all kinds of stuff down there -- the floor will still get wet during heavy rains.  But it's a big step, and very satisfying, and our insurance paid for it!  :-)