I never thought of that! Good analogy.
The solubility of a gas in a liquid decreases with increased temperature. CO2 in the atmosphere follows warming events, just as in your warm Coke example.
How long after intensified solar heating does it take for the warmer upper layers of the oceans to mix and distribute their heat? Many seasons will pass before the cooler regions begin to release some of their CO2.
The oceans are a huge CO2 sink, and it is more complicated than simple solubility, because the oceans are buffered. Every clam traps CO2 as calcium carbonate.
This is a sensible explanation for the built in time delay.
The solar researchers cited have managed to flunk both Thermodynamics and Chemistry, but never mind that. They FEEL the right way, and the motives are noble.