Try and follow the directions as closely as possible. I have not grown any
Stropharia or
Coprinus comatus, so take my suggestions with a grain of salt.
I would put each one in a separate bed. Avoid adding any dirt, if possible. These
mushrooms are decomposers, they eat dead plant material, not dirt.
If you use mulch with the
Stropharia, don't use too much - keep it mostly woodchips. Keep any mulch separated from the spawn by the woodchips.
I would suggest building "sandwich beds" - first, put down a layer of
cardboard, then your woodchips (or mulch), then your spawn, then more woodchips (mulch). (See Paul Stamets' book
Mycelium Running for details.)
The
Hypzigus ulmarius will do fine with woodchips or mulch - I would suggest mixing some woodchips in with the mulch to get a longer lived bed. (Which will hopefully inoculate your Hugelculture logs for a self-perpetuating bed.) I have grown
H. ulmarius with just sawdust and woodchips and must say that it is one of the most vigorous and productive mushrooms I have ever seen.
Elm Oyster mushrooms ready to pick by
frankenstoen, on Flickr