I’m not sure if this is the cause of my current issue but you have good intuition. When I first set the system up, it would not reasonably carbonate, as if there were no carbonation stone in place. It hit me that the tank was air filled when I forced water and CO₂ into the existing atmosphere under pressure and that might be interfering with the carbonation. I purged the tank a few times and a couple hours later it was carbonated.

The carbonation charts and calculators assume that the headspace is 100% CO2. If you start with CO2 at atmospheric pressure in the headspace the gauge pressure is 0 psi, but the absolute pressure, and CO2 partial pressure, is 14.7 psi. If the chart/calculator says you need 20 psi for your desired carb level, and you set your regulator to 20 psi and connect to the keg, then the absolute pressure in the keg (and CO2 partial pressure, is 14.7 + 20 = 34.7 psi. The equilibrium carbonation level depends only on the temperature and CO2 partial pressure in the headspace. So, in this case you need a CO2 partial pressure of 34.7 psi to get your desired carb level.

Now if your headspace starts out full of air at atmospheric pressure, and you connect CO2 at 20 psi, the total absolute pressure will be 34.7 psi, but the CO2 partial pressure will only be 20 psi, and you will be under-carbed.

If you start with a sealed keg full of air at atmospheric pressure, and you force water into the keg to 3/4 full, the absolute pressure in the keg will be 4 * 14.7 = 58.8 psi, and the gauge pressure will be 44.1 psi. If you connect CO2 at 20 psi, nothing happens if you have a check valve on the CO2 line, or if you don't have a check valve, air flows back into your regulator. In either case, no CO2 flows into the tank, you have 0 psi CO2 partial pressure, and you end up with 0 carbonation.

If one were to conduct a thought experiment with two kegs, one with a low pressure and one with high pressure, the tank with the lowest pressure and thus highest differential will have the greatest potential for work. That work will be realized as transfer of more gas into the keg and into the water inside that keg. It takes energy to move CO₂ into solution and that energy comes from the pressure differential. Thus, although both tanks would reach pressure equilibrium, the tank with the lowest starting pressure would undergo the greatest work, the greatest energy (gas) transfer, and thus have the highest carbonation level.

It doesn't work like this. As stated above, the equilibrium carbonation level depends only on the temperature and the CO2 partial pressure in the headspace. The starting level of carbonation in the liquid does not affect the final equilibrium, but will affect the rate at which CO2 is absorbed.

Brew on