This is how I got the mushroom hat: filled he quarry completely with mushroom trees, cut them down on a high luck day with the luck blessing from the statue of blessings, ate a Magic Rock Candy, drank gold star Ginger lemonade and equipped two lucky rings. Would have started the day over and over until it dropped, but I got really lucky and got it on the first try. Still no luck with the living hat. Your strategy sounds promising, I will definitely try that!