I keep reading that oyster mycelium, once it has grown some, will out-compete other organisms. To what degree is this true? Will it eventually push out green mold?
Oyster mushroom mycelium will definitely NOT out-compete green mold in anything but the most nitrogen poor substrates. Even then, it is usually just a race to get the mycelium to the point of fruiting before the mold starts to take hold. And although some molds are harmless, there is concern about consuming mushrooms from substrates that have begun to mold.
And once you start fortifying straw or sawdust with nitrogen (whether through molassas, alfalfa, or some other source), the chances of losing to the mold increases.