...I'm confused. How can it be the driest, hottest, and most humid period ever?
:d

)
By the way, I doubt that any kind of climate can cause an instrument to rust quickly, unless you let your instrument outside on the shore for some time, or let it all the time in your band practice room (especially if the practice room is 20m², host several sweating bands, and as no aeration)
It is more than normal that your Brass nut tarnish. You can polish it as much as you want, after a couple of days, it'll be tarnished again, unless you varnish it. That's brass.
Then, I would not use any abrasive product on your hardware (brass polish like Brasso or stuff like that). You'll just remove the plating more quickly...
Most of the time corrosion is due to the player, and the only thing that helps is to use a soft cloth to clean it after every practice. WD-40 might help to slow down the corrosion, but I'd tend not to recommend it. The only thing I'd spray on an instrument would be Dunlop 65 (unless it's a Gibson, on which I would not even spray something).
But send us pics of the corrosion, and tell us where is this dry and humid place where you live! ;o)