I'm not familiar with the Back To Eden method, or how it differs from just using a couple inches of wood chips to mulch with, but I can say wood chip mulch works very well for me in Central Texas. Cedar chips are a little less effective from a "feed the soil" standpoint, as they take forever to break down, but they do a good job holding in water, and keeping soil temperatures down. Just about any other hardwood chips work great, but I would recommend using chips that have composted a little. If you have a source of fresh chips, like from a tree-trimming service, I'd let them "mellow" for a few months before using them, so they won't be too "green" (in the nitrogen sense) for tender plants.
We usually just buy composted hardwood mulch a truckload at a time. It's only about $25 for a cubic yard at most of our local landscape supply places, if I recall correctly.
If you have access to a lot of shredded leaves, I've found that putting a layer of shredded leaves down, and covering that with the wood mulch works extremely well. The decomposing leaves seems to attract earthworms and other soil life much better than just wood chips alone.