I had mushrooms pop up on my compost pile after wetting with JMS  

Leaf mold soil is great for fungus too because it is also static (like Johnson-Su compost), and has access to moisture and air.

However, leaf mold soil has more advantages: it is where the organic matter meets the soil (sand/silt/clay), it is where the aerobic meets the anaerobic, it is where the wet meets the dry. For these reasons, JADAM views leaf mold soil as the perfect source of microbes, with the ultimate diversity for the farm.  

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.  

A bioreactor wetted with jms, and a catchment underneath to catch the run off and use as fertilizer. Basically creating your own leaf mold soil if you inoculate it after the initial hot compost period?  

I watched a video by Johnson-Su Bioreactors.
It's too complicated for me to follow. I recommend JMS.

I don't think that a complicated method is necessarily a good thing.