Recycled oil is recycled oil and is sold as such. There is no such thing as "natural recycled oil" and "synthetic recycled oil," it all gets thrown into one bucket and recycled. There is no reason to separate the two.
When you recycle oil, it gets dewatered, evaporated, and hydrotreated before having whatever anti-foams, dispersants, and detergents added back in. For all intents and purposes, the "recycling" process is no different than the original refining process. I guess the only difference is that some molecules were naturally made, and some man made. Functionally, for the consumer, any quantity of recycled oil will be no better than full synthetic and no worse than full dinosaur. It's a distinction that probably isn't worth making.
Edit: And that reminds me - another reason why super-extended oil changes are not advisable is water. At a typical ~5,000 mile oil change your oil may be 5% or more water. The reason big bypass systems have heaters is to get that water out. Without a heater, you will accumulate water in your oil. As you can imagine, that is not good for the engine.