one could install a conductivity controller on the aquarium and that could switch on and off a freshwater supply to regulate the salinity in the aquarium
Excellent idea. The Profilux you have can do this. You can even have a secondary parameter to shut the pump off, such as PH, temperature, or ORP.
Alternatively, you can monitor tank parameters and use them to govern when larger water changes are necessary; for example, if your ORP, PH, or salinity/TDS fall out of line you could have the controller turn on a second pump from the sea for greater turnover. All this can be done with the ATO function.
Monitoring the water level of the display and topping it off with pure freshwater will also keep the salinity and subsequent elements stable, at least from a concentration standpoint.
As mentioned earlier in the thread, you need to add the elements that are in deficit, if any (calcium, magnesium, carbonates, strontium, iodine/iodide etc.), and remove anything that is in excess, including the ones listed above through dilution (freshwater) as well as any excess nutrients (nitrogen, phosphates, silicates, bacteria etc.). The latter can be assimilated/dissimilated by a mangrove or seagrass trench, ozonation, UV irradiation, mechanical filtration, and carbon. If you can find a cost effective source of activated carbon that is low in phosphates and nitrates it will be the most effective method, as it can remove 80% of the TOC (total organic carbon, including particulate/POC and dissolved/DOC). Carbon is the best tool for turning yellow water, rich in tannins and pigmented organics, into crystal clear water without removing the "good stuff" such as salts. It can however remove too much "good" bacteria, but not in a single pass as the seawater is imported into the display tank.