This is my own design. It is possible for the farm to overflow with bonemeal in the two barrels on the minecart contraption. To stop this I only supply bonemeal to it when its running and one at a time.
This farm doesn't work immediately out of the box. I got it to work after breaking and replacing the deployers and redstone links, and adding a minecart to create the contraption. Also make sure to give the mushroom space to grow.