I use both dunnage (unprinted newspaper) and single face corrugated for ease of cleanup. The 'brown paper' is probably kraft wrap, I find that to be too stiff for my liking.
I could possibly see it helping lower humidity since it doesn't do anything to hold/capture humidity.
Another thing that helps lower humidity is more air flow in/out of the cage. I'm battling this in one of my stacks and once I move, I'll be drilling a bunch more holes in the caging which I expect to help with the issue.
If you want to stick to a loose substrate, try aspen instead.