watch this. he explains that most atmospheric CO2 comes from natural sources. he runs through how the cycles actually work, the delays... what you call 'sensitivity'
btw, your entire "senstivity is linear" line rings my bullshit detector. big time. It comes across as your excuse why predictions made by alarmists 20 years ago have not remotely come about
what appears to happen is heat causes CO2 to break from ground water. some atmospheric CO2 comes from heat- NOT THE OTHER WAY AROUND ONLY.
this is why the PPM from 1860 is like that, why it has not driven temperature. the temperature (emerging out of an ice age) has driven the PPM.
a huge chunk of your causation is backwards. ASFAIK