Any drift seen on the pH meter is drift in the glass and reference electrodes.
Have you ever had a taste of soda water? If so, why is it "tart"?
If you put dry ice in an open glass, let it melt (actually sublimate), then taste the water, you'd discover that the water tastes tart -- because of the carbonic acid that dissolves in the water from the dry ice. The pH has to change when this happens. Seawater pH will change less, because of the buffer system. But it will change.
Hunble, this brings up a safety factor. I'd suggest doing this experiment in a plastic soda bottle. Add the dry ice in little pieces, then put a balloon around the neck of the bottle and affix it tightly with a rubber band. The ballon will inflate some, but this will keep the headspace charged with CO2 while greatly reducing the explosion risk.
Soda water is a supersaturated solution of CO2 in water. It's pH is 5 something, as is distilled water that's been exposed to the atmosphere. Once the cap's off the soda water it will release CO2 until the equilibrium conc. corresponding to the atmospheric conc. is reached.
"Seawater pH will change less, because of the buffer system. But it will change."
Seawater pH is 8.1+/-0.1, that's good enough. Calling a change within that range acidification for the purposes of justifying "serious problems" for coral is flat out BS. That's the findings of the research, which is mentioned in that paper above, which fails to include mention of the complete local system in fig2.
Once all the components of the system are included, there is no net change in CO32-, because the increase in CO2 causes an increase in dissolution. As I pointed out, the same increase in dissolution occurs locally when alkaline carbonates precipitate to form the corals. IOWs pH does not depend on alkalinity in the real system, it depends on the saturation conc of the alkaline earth components Ca and Mg and all the various dissociation constants.