Your system just needs an increased level of nitrogen (nitrate) export. Don’t expect to control nitrates with activated carbon or skimming. They are playing a smaller role. I assume the marine pure bricks are suppose to increase denitification capability (NO3 to N2), but they might not have the capacity you need.
Caulerpa removes nitrate, but how much depends on light intensity, micro nutrient availability, water motion and how much you have. If the Caulerpa is not doubling in size every week or so, it is underperforming.
Carbon dosing, vinegar or vodka, would be a cheap and easy way to increase the nitrate export capability of the system. If you had an automatic doser, even easier. If you follow the dosing schedule of the table on the internet, it is probably the one that has been incorrectly scaled. If you follow it, the increase in the dose will be too slow and you will never reach an effective dose, i.e., carbon dosing will appear fail.