The fungus needs 4 things to grow: food (the wood fibres), moisture, air and limited amounts of light. There's nothing you can do about the food. You can limit the amount of moisture by not allowing any more moisture into the wood. You can expose it to lots of light (but avoid excessive heat, you don't want the wood to dry out too fast, and you can cut off the air supply by dousing the entire piece of wood in a coat of PVA. There will be some initial oozing, yes, but it should stop quickly.
It's always a bit of a gamble, and not all fungi work at the same speed or produce the same result. A block of wood of these dimensions will take a looooong time to dry (according to rule of thumb at least 12 years), and unless you are likely to use them for large pieces of work, it's probably better to cut them into usable blanks, and then go from there. Or do the rough turning in the green and then dry afterwards.