Is there also a connection from the observation that fasting is beneficial because it forces our body to burn our fat stores causing the release of deuterium depleted water from within our own fat cells to fuel healthy mitochondria?

This is a nice theory but is not a major source of deuterium depleted water. There are other consequences, mostly affecting the metabolic function of mitochondria and the need for a ramp-up in oxidative mechanisms that could be destructive. In avoiding those pathways, the system is able to maintain a more normal balance and this confers a health benefit rather than to be a kind of onslaught that impairs the body through having to cope with an inadequate and unnatural source of nutrition.