Oh. Sweetie. I feel for you. Finger's crossed for the promotion!!
I used to work in a very humid studio and found I was constantly fighting off colds. The quantity of water the dehumidifier would pump out was amazing.
As for the latex issue, if you clean the mold with a baking soda solution you don't really gloves. But try using a plastic bag on your hands. It's not super practical for detail work. But should be fine to hold a sponge and wide down.