Welcome to the forum , Flightfanatic .
It sounds like , from your posts , pages/bindings & unseen elements are affected by the malaise .
Being as you asked about a safe way to clean/restore/stop damage on your item , I think that it's a matter of how much , and what parts need repair .
I kinda calculate things like - how much damage & what type , is the item some piece of history I feel prompted to preserve , is it the items' value that I'm trying to preserve , how much damage will restoration cause & so forth - when I see damaged/restorable items .
As I see it , you've got a damaged item now .
It also sounds wise to remove it from your safe ( as well as reconsidering storing humidity-sensitive items in it) .... might be time to bleach out your safe too , for starters .
You can @ least get it (your book) into a better/dryer environment , as others alluded to .
"Big-time" book restoration is not for the impatient , faint of heart (or pocketbook) or the uninitiated to attempt , in this old mans' opinion .
If you're looking to learn , perhaps this rather fragile one is not the one to start on ......but then again ...