A dehumidifier cabinet definitely seems like an effective way to battle this problem. Unfortunately, from what I've found it's also pretty pricey. And I don't know if I'm just not using the right search terms, but after a few minutes of Googling (isn't it weird that word is now kind of common place in today's society?) I can't find any manufacturers or suppliers in the US.
Luckily, my job in our local (and only) camera store has me privy to lots of stories from many photographers. One such photographer is Zane Mathias. He lives in a really damp and humid area of Maui and has had this problem. He came up with his own solution, which, while not as elegant as a DigiCabi, definitely has worked for him:
Check the article on his invention here: Beating Lens Fungus
As for how long it takes mold to grow in a lens, that's kind of relative. It depends on so many changing factors that can vary not only by location but from one day to the next. The biggest thing to remember is that if you're in a humid environment, don't move your camera or lens between high and low temperatures too rapidly. If you do, condensation can be created and that's what will help lead to mold. In fact, all of Canon's manuals say the following:
If the camera is suddenly brought in from the cold into a warm room,
condensation may form on the camera and internal parts. To prevent
condensation, first put the camera in a sealed plastic bag and let it adjust to
the warmer temperature before taking it out of the bag.
That was taken verbatim from the Canon EOS 1D Mark IV instruction manual. And yes, L lenses can grow mold, too.