So you're pretty sure it wouldn't exist even without all your assumptions (150 year carbon cycle, etc).
But there aren't fast mechanisms that would cause such a big CO2 excursion -- unless you'll be able to surprise me with one.
There are undoubtedly fast natural processes that will create sharp albido changes, temperature changes, etc which, without making prior assumptions, could cause large CO2 changes.
"However, tucked away at the end was a rather confused section, where it appears that Lindzen bet Nye that ice cores don't have a resolution better than 2000 years. Now this is an odd claim, and an odder thing to bet on, since Greenland cores (GRIP, GISP2) and Antarctic cores (EPICA DML) have sub-annual resolution in many cases for the isotope (temperature) records, and at least decadal resolution (Law Dome, Siple Dome) for the greenhouse gases (CO2, CH4). It's true that the very longest records (Vostok and Dome-C) have coarser resolution, but surely Lindzen doesn't think they are the only ones that exist?"
Based on that, it would appear that some ice cores could provide data indicating 80-100 ppm CO2 excursions on the century scale -- if they ever happened. Note that this includes EPICA, the 650,000 year long core.