Is there any natural phenomenon that can account for the 100 fold faster CO2 rate increase?
There are things that could do it, but they would be very noticeable. 


A whole string of thousands of the largest volcanic eruptions to ever occur on earth. Volcanoes can briefly match human output, but volcanoes only erupt for a few minutes or hours. you would need the equivalent of mount St Helens erupting continuously for 70 years.  
The burning if every forest on the planet. I'm sure humans would notice such a firestorm, and I;m not even sure if that would be enough. 
The slow extinction of photosynthetic algae. without the bulk of photosynthesis to convert co2 into oxygen it could build up. Of course we monitor this so it would not go unnoticed. More importantly oxygen levels would also drop dramatically which it hasn't. https://scied.ucar.edu/imagecontent/carbon-cycle-diagram-ipcc 
The ignition and continuous burning of millions of miles of exposed coal beds. You would need to burn approximately ~3 teratons of coal. coal beds can be ignited by natural causes but we would notice a coal fire larger than a continent. 
A drop in sea level by hundreds of feet would do it. large sea level drop cause outgassing of methane and co2, from wetlands and sea muds. but again New York would notice it if long island stopped being an island. 


Some of these have actually happen in earth's geologic history just none recently, and not as consistently as we have managed (at least not since life evolved). Really scientists have spent a lot of time and money looking for other causes, and no one has found any. Scientists concluded it was human activity by eliminating every other conceivable cause.