You're low on coolant, did you top it up after the first episode?
No, it doesn't work that way. As i pointed out a bit further up, the system is designed so you can use or not use the heater and it doesn't alter the engien cooling at all.
At the risk of making a snap diagnosis, i'd suggest the main radiator is either blocked or leaking if the head gaskets have been ruled out. Also worth trying the radiator expansion tank cap. I had a similar thing with mine where the coolant would be at the right level but the heater was blowing cold, it turned out the cap had gone weak so was allowing coolant to escape when it shouldn't which created airlocks. Because the heater matrix is so high on the S Type, that's where airlocks show up first. Worth trying one and topping the coolant up to the cold mark before you use the car each day to see if it's as simple as that :
https://www.ebay.co.uk/itm/403748795978
If nothing else, it will eliminate that as a possible source of coolant loss.