With the back to eden method, its not a lot of messing around to achieve it. Keeping things layered is ideal. Mixing will increase the composting process temporarily but adds more work, destroys soil structure, eliminates fungi, and reduces drainage.
When you add organic matter to a rich compost, it will start sapping nutrients from the soil to process the organic matter. This reduces the nutrients available to plants until the organic matter is processed. The larger the surface area, the quicker the decomposition process. Some materials like bark are resistant to decay and won't lock up the soil as much.
To combat this, adding a water soluble nutrient (fish emulsion, urine dilution) to the
root zone of the plants will allow them to uptake it directly. Do this on a dry day if possible to allow the
roots to take in the nutrients before they wash down into the soil.
Another alternative is to add a organic "slow release" garden fertilizer and apply it in the wood chip layer. This would
feed the bacteria/fungi as they go and not tie up nutrients at the root layer of the plants.
Compost tea can be added monthly to keep everything moving quickly.
Mulch Layer
This is above the root layer. This can be anything with
carbon (wood, leaves, dried grass stalks)
Compost/Organic Matter
This can be planted in. Minerals can be lacking in this layer. Carbon rich wood lacks a lot of minerals. Adding rock dust or soil to this layer can increase available minerals. Can hold 7x its weight in water.
Soil
This is mineral rich, but not a lot of organic matter. Roots are shielded by the organic matter and mulch, and have good drainage.