Shiitakes are a bit of a pain to grow on paper and cardboard waste, I'm not surprised that only the oysters grew, they are the easiest to grow in such a small scale low tech environment. If you have access to okay or poplar saw dust that is a good material. used coffee grounds is also a decent option. To sterilize those you could just boil them, and let them cool three to four times before straining them and adding them to your plastic container and inoculating. You should also add a supplement to raise the pH to make the coffee grounds a better growing medium for shiitakes. A little oyster shell, which you can find at any gardening place, will work just fine.
As far as contamination goes, you'll almost always get some using a method like this, if you're opposed to bleach, then hydrogen peroxide will also work, or you can use 70% isopropyl alcohol which instead of changing the pH or oxidizing, it breaks down the cell wall of organisms. However the container is not your only source of contamination. Make sure you clean your hands very thoroughly before touching any of your materials, try not to leave them in open air too long, and do your best to wipe down the mushroom stems as best you can with a sterilent (Not a heavy amount and not bleach, just wipe the outside of the stem before you tear it apart) before using them.
Hope this helps, if you want more details just let me know.
