Johnson-Su compost is nothing special, it’s a static pile with water and some air. That’s why fungus likes it.
It would probably make good JMS, but you only need a handful even for inoculating large areas. Besides, the layer touching the soil is most important in JADAM’s view because you will be inoculating the soil. Why make a whole special bin?
It’s equally effective, and much easier, to collect leaf mold soil, or make your own by layering grass on top of the soil and keeping damp.