Just make it a trade secret? A patent is basically making it public in exchange for a guaranteed, albeit short term, exclusive right. Why not just let only a few know and keep it secret from everyone else?
If there was a reliable trade secret, then there would probably be farmers producing outsized yields. Hiding the total production per acre would be difficult in such a top end product where consumers frequently tour the farm.
Edible foraged mushroom markets are surprisingly opaque. The foragers are unlikely to give anything more than a vague notion of where they find their stuff in my experience.
It wouldn’t surprise me at all to learn that there are people that have figured out how to increase yields in the wild or simulate correct growing conditions
Lots of businesses have successfully kept trade secrets for decades, many very famous and gigantic company's recipes are trade secrets. Companies know that if they patent it, it will be in the public domain eventually, whereas trade secrets can stay secret indefinitely, theoretically.
The vast number of off brand cola and waterproof fabric products would seem to imply that marketing is the operative force rather than the secret recipe.