If I'm understanding you correctly, I'm not sure humidity under a small (relative to the rest of the apartment) dust cover would amount to much. It's not like the humidity will get trapped in there by the humidity equivalent of a Maxwell's Demon or anything -- as much humidity departs as enters if it's not hermetically sealed, and if you had it on recently when you put the cover on, it'll probably be less humid in the vicinity of the amp than elsewhere in the apartment.
Heck, it was probably exposed to more humidity in Justin's workshop in swampy ol' Virginia while it was being built than at your place.
I thought you all had dry heat? And by you all, I mean West of the Mississippi (and East of the ...whatever mountains that stop the humidity rolling off of the Pacific -- I know it doesn't take much, my sister used to work East of the bay, and it was basically desert there).