Growing King Stropharia outside is a good idea. They are the prototypical "mushroom patch" mycelium. They need bacteria to be able to grow. Airing out your water so it can get rid of the chlorine is a good idea. Many municipal systems also have chloramines, which are more persistent and won't just gas off. They can be changed by adding
enough compost to give the water a slightly brown color. Be careful when you add a lot of water. Be especially careful if your mycelium has nearly eaten through the substrate, because when I did, they decided to fruit the next few days, and for part of that time, I was out of state on vacation.
John S
PDX OR