That sounds generally correct. A mutation doesn't have to involve the creation or destruction of a new gene, it can be at the level of expression, or not, of an existing gene. Evolution by turning on or off a particular gene would, I'd expect, be faster than evolution by editing of DNA, which fits Sawyer's thinking above about evolution evolving better methods of evolution. That may be the conceptual explanation for your observation that the rate of evolution seems to have increased over time.

Note that this kind of evolution depends on diversity inside the individual genome. There's a second level of that kind of diversity, in terms of the variability of individuals within a species. The broader the variability within a species, the better able it is to survive--as a species--when the environment changes.

When you extend this idea into the human noosphere, it becomes apparent that social and cultural diversity confers very much the same benefit. A culture is a body of ideas and beliefs which are more-or-less functional when measured against reality. When reality changes, ideas/beliefs that were advantageous may no longer be so beneficial, and another set of ideas and beliefs is selected to come to the fore as the most powerful way to think or act; the most adaptive, in other words.

I have to take issue with your use of the term "evolutionary tree". It implies directionality to evolution, which leads so many people into the error of thinking that evolution is "pursuing perfection", as if evolution were an anthropomorphic personification with a particular goal in mind. It's the misconception that enables the silly argument about "Intelligent Design". Evolution pursues only local optimization, local both in time and space. Today's local perfection is tomorrow's deceased misfit.