I would venture to say that the decomposition process itself (using wood chips as a mulch on top of the soil) has a lot to do with its beneficial effects on soil. I haven't seen the Eden video but just from what I know about wood decomposition.
Once things are fully composted, the final product is more similar than the different ingredients one may have started with. So I'm not sure a wood-based compost will be that much of an advantage.
Also, the fact that it's so slow to decompose is exactly why they add other ingredients. You're not likely to find what you seek as it's not economical to wait that long.