I looked a little further into the CO2 pressure needed to dissolve chalk. I took the data from Wikipedia
and plotted it into chart with logarithmic x and y axes. Ther formula that approximates the data well in the range that is of interest for us is
[p in kPa] = 8.71e-8 * [CaCO3 in ppm]^3.24
This means that there is a dramatic increase of the pressure needed as the concentration of chalk that needs to be dissolved is increased. In practical terms this limits the chalk that can be dissolved by the soda bottle or keg method to about 880 ppm and with it sets a minimum amount of water that is needed to practically dissolve the chalk. I'm adding this calculation to my spreadsheet. To dissolve that concentration of chalk about 3 bar or 45 psi of CO2 are needed. This includes the ambient pressure which means you would have to set your regulator to at least 2 bar or 30 psi.
Here is a chart I made that illustrates the relationship
It also shows the chalk that can be dissolved by the CO2 in ambient air and a pure CO2 environment at atmospheric pressure.