I can't speak specifically about the companies or products you mentioned, but I am a firm believer in the value of the microbial life forms in our gardens. I inoculate most new plants with mycorrhizal fungi. The threads of fungi/mushrooms do a tremendous work on the wood in hugelkultur beds. I do everything I can to encourage that.
About your anaerobic environment: A hugelkultur bed, even though buried in soil, is still very much aerobic, more so than an average garden, actually. The action of earthworms moving through the bed is like a piston, bringing air in and out of the bed. Dig around in a good hugelbed and you will see the evidence of air and life.
Legumes properly inoculated with rhizobia bacteria will produce lots and lots of ammonium nodules, evidence of the atmosphere present in the soil.
