Well, my mushrooms are growing!
I bought a box of growing oyster mushrooms about three months ago, which gave an acceptable pair of crops, as advertised.
After that, I obtained a couple of days worth of my work's coffee grounds (we drink a lot). I broke up the remaining mycelium-impregnated medium from the box and stirred it in to the coffee grounds. The mycelium regrew for about three weeks and has just started putting up mushrooms. No idea how long the fruiting will last, and you can't continuously take bits of mycelium and throw it into new medium. At some point you have to get a new fungus by sprouting mushroom spores on agar gel, letting them cross and then transplanting the new mycelium to growing medium. Not sure I want to go through all of that, particularly as I discovered after the original box fruited that I don't actually like oyster mushrooms. They're a bit fungussy for me.
But I'm proud of the new mushrooms. I didn't even have to case them - the pressure of the medium against the enclosing plastic bag seems to have set them off growing by themselves. The thing that looks like molten lava in the middle of the bag is just a coffee filter that got in there by accident.
After they're finished and the mushrooms thrown tidily away, the remaining used coffee grounds will make a nice mulch for the yard.