In my experience putting a plastic (non-breathable) layer over metal intensifies rust and pitting.
As you say, I also use the rag-in-a-can every time you put your tools away. Make sure you at least blow the wood shaving off first too, as they will contain moisture.
Also, do regular maintenance: I keep an eye on my tools and tidy them up with a scotch bright pad now and again, then re-oil.
Lastly, cardboard will retain moisture. Unless your cardboard is 100% dry I’d try to find some plastic boxes and add in some desiccant pouches.
I live in a damp environment and this is is what I do.