I'd certainly limit the space when not at home! Mine is a climber too, and it sucks when we can't leave them in one room while we're gone.
I know it doesn't work on all, but I use clear deoderant on anything Venus starts chewing on. She's chewed a hole in my lenolium, working on basboards, one outside corner of the room. Seems everything I put the deoderant on real well....she only goes back to one time, after one taste

she changes her mind.
So my kitchen is now very well deoderized and shouldn't stink when sweating
I also give her something else she likes to chew on real good, like those pig ear looking things. Find something your pup loves to chew on, that will last a long time. Thats helped some with me.
But seems for Venus, nothing works like a good coating of clear deoderant! I know a few here, it doesn't work on, but it does on Venus.