It is very unlikely to be the SSR, those device are quite robust and since triggered, theire internal resistance are very low, there is no in between. The brewie controller modulate the power (PWM) to the SSR like a top of the line PID would do but when the target is to boil, there is no raison why the trottling came from there too. Your problem is, like you said, comming from the thermal switchs or/and the connections that get too hot (connection get hot ther bring heat inside the thermal switch). As I said earlier, the ventilation of the area around the connections is the only way to realy make the thing work. I stop the water heating during my test without venting with the thermocouple when the water was at something like 65 celcius, cause the therminal were already at max temparature. Since the terminal raise in temperature, it lose grip on the connection and contact resistance raise, with 4 crimped connection, so 8 jonctions, it can surely lower the power to the element.
I should recieve as a gift ;-) a water heater for vaccum cooking (kind of rod with an impeller and a heater), 1200W, and i'm planning to use it to help the brewie to heat and boil water, as well as vaccum cooking ;-)