Nope, you can just let things coast along. If the mushrooms get slimy and disintegrate over your greens, you can just pull them. They're actually helping the straw and compost decompose into nice soil. I've often wondered if a straw bale could be inoculated with mushroom spawn, so you could...
You can cycle them quite quickly by giving them a healthy dose of Ammonia, Urea, or a high nitrogen fertilizer. I had good results with the technique, but found that it required more frequent watering than I cared to do. I actually had better results with hay bales.