Growing oyster mushrooms on cardboard. I have tried it. I failed at it :) I'm reasonably confident I know why the experiment failed and how to make it work.
What I tried to do was, in essence, continually collect all cardboard and junkmail that came to our site into a large wire bin. I had already collected something over a cubic meter when I tried to inoculate the pile with oyster mushroom spawn. This was not Good Planning ;) The material could not be mixed to get the spawn distributed and it also was not possible to actually get that mass of cardboard and paper anywhere near as wet as it needed to be.
On a small scale, like the buckets up
thread, you can absolutely soak the cardboard and the volume is small enough to inoculate effectively even if it won't mix in.
If I try it again (when, who am I kidding?) I'll collect a few pounds of material, totally saturate to where it is breaking down, inoculate that and then continually add more wet substrate.