I'm on board with your view that we are a part of nature, not separate, but when I think of previous speed-ups in rate of change (i.e. sexual selection to allow more rapid gene reshuffling, or epigenetic modification which allows more flexibility from the same genes) these have been spread across multiple species.
The acceleration we are currently seeing is basically due to the industrial revolution, which is due to people finding an net energy positive fuel source and leveraging this.
Nature is a chaotic system, yes, but chaotic systems have balance and tend to have semi-regular orbits.
By so drastically changing the rate of change past what any other living thing can match, we are on course to push the system into a new regime. Which is unlikely to be as pleasant as the one we currently enjoy.