I was more aiming my arrows on this, since i live close to the border i have a German delivery address, no international shipping cost as local a pic up.
Probably, i'm not into the mater enough to say something conclusive about it.. As said each 10mm down is a 0.0001 bar pressure buld up. If you can speak of a pressure increas, relatively.. I have no idea on the numbers of the force needed for co2 compresion as in boyls law. There obviously will be a form of counter pressure by the gas. I would need to dig realy hard for numbers and formulas. To calculate which force is the greatest.
For now obviously the upwards pressure on the co2 in the vacum is 1 atmosphere. If the level of co2 is 15cm bellow the surface it will be 1.0015 atmosphere.. I guess the whole only can be theoreticaly calculated without an accurate barometer measuring the invironmental air pressure which next to that never is constant. Without it we assume it is 1.. If it isn't you always will be a few 1/10000 units off.
Neglecable if you ask me.. If it wasn't we didn't use 1 as a starting point for calculation. And an atmosphere pressure sensor would be common tool as must have.
Your estimate is too simplistic and can't be correct. When you open a can of soda, CO2 bubbles are released due to reduced pressure. CO2 is under slight pressure in the can, probably no more than at the bottom of a fish tank for safety concern.
Boyls law defines the relationship of gas pressure and volume. It's a universal law applicable to all gasses. The relationship of CO2 solubility and pressure is governed by the properties of specific gas (CO2 in this case) that vary from gas to gas. There are also other influencing factors such as temperature, partial pressure of CO2, and concentration gradient at the air water interface. It's complicated and the only sure way is to figure out is to conduct experiments to compare CO2 concentrations under different depths.