... you've posted an article conceding there is 450,000 years of correlated data, you don't even dispute the correlation, and your concern is about the *strength* of CO2-induced warming?
The correlation indicates (but doesn't prove) that colder temperatures cause CO2 levels to drop and warmer temperatures cause CO2 levels to rise. That makes temperature the driver. (if you accept that a correlation is proof of causation)
But the opposite conclusion, that CO2 levels drive temperature changes, is impossible. Cause always precedes effect.
A reasonable theory can easily be constructed to account for temp. changes causing CO2 level changes. The planet cools and plant/animal activity decreases leading to lower CO2 levels. The planet warms stimulating plant/animal activity and CO2 levels rise. The long lag between temp. change and CO2 level change reflects the slow and measured response of dense concentrations of biomass (jungles/forests) to temperature changes. The CO2 levels are driven by biomass levels which are driven by climatic changes.
First cause, then effect.
If CO@ levels are following temperature changes, then that tends to strengthen the possibility that bolide strikes and supervolcanoes may be causing some of this.