I usually sprinkle a bit of dirt and/or some of my last batch of compost in my pile every now and then. Sorry, don't know anything about mycelium... Is this something you buy to add in, or something naturally occurring?

You need to be adding celulose based material for most fungi to thrive (wood shavings, *small chips, paper or cardboard)
Oysters kits suggest you mix into compost piles when they are nearly spent, but you want some straw/ sawdust or paper/cardboard to help in the pile
though you want oysters to completely break down the pile as they aparently will parasitize plants if still runnign throug hthe material when introduced to your garden
Garden Oysters will acutally help break down material (like straw) right in the garden and increase the

fungiperfecti sells garden oyster kits as well as their "3 Amigos" kits
The most frequent voluteer in my compost piles have been inkies- they are fairly close to the shaggy manes so I would reccomend giving them a shot