I've used shiitake, oyster and portabella bought from the store right here in California U.S.A. to generate cultures with success.
I've messed around with card board a little bit but I'm not sure what you're referring to, but the card board method works best with the mushroom stem butts.
As far as what I did it was just a traditional live tissue culture on agar using sterile technique. Its helpful when using store bought shrooms to first wipe the outside of the fruit with peroxide before cutting it open. When you make the incision and cut out a piece for the agar, dip the piece that you are going to use, dip it in peroxide before placing it on agar. Let the peroxide
drip or dry off a bit before setting it on agar.
The portabella culture (which would have yielded the common white agaricus mushroom) did not fruit, because I used the spawn to colonize sterilized grain. Ports wont fruit on a sterilized substrate because they require the presence of actinomycetes which are found in
compost and pete moss among other materials which I didnt use. Pasteurization is the only way to grow ports.
One shiitake that I tried to clone from a store did not grow at all because it was one of the strains bred so that they cant be cultured by another grower.
Once I grew oyster mycelium on
cardboard, but it wasn't moving along fast enough for me, so I took a piece of cb that had mycelium growing and transferred that to agar. Once I'd generated spawn with that (via the agar wedges), I nocc'ed up some meadow type grass from an empty lot in a small northern cal town, that had been brushed with a weed eater. It contained wild oats and other common grasses, wild radish and brown leaves. Didn't yield well but it was fun.