I used to live in an apartment that got up to 90 during the summer. I bought a 150qt cooler and put my humidors in the cooler. I also put an ice pack wraped in a towel in the cooler and changed it daily. Doing that will keep your cigars cool without sucking all the humidy out of the air. It worked pretty well, and then I filled the cooler with cigars, and had to buy a house with AC. It may sound crazy, but so does digging a hole in the back yard for your cigars.
The best advice in my opinion is to freeze them and move on.