The warming isn't unprecedented. It's natural for a deglaciating northern hemisphere. You need to look at the data for the Arctic. Lot's of temperature increases and decreases.I understand the mechanism you’re describing.
The distinction is that this explains past natural fluctuations and regional differences, but it doesn’t explain the unprecedented rate of global warming today. Human driven CO2 emissions are increasing atmospheric concentrations faster than natural processes have ever done, which adds a radiative forcing that is independent of these regional ice thresholds. In other words, even if ocean circulation continues to redistribute heat, the background warming is being amplified by anthropogenic greenhouse gases.
δ18O from the GISP2 ice core for the past 10,000 years.

