Adequate heat sinking should control the solder from reflowing. This too is an appliance control application. I have examined several pcbs for similar products and also much higher currents ones(cooktops). They all hold up, the cooktop has massive heatsinks on two mosfets that share the load.
The issue with my dishwasher is that the relay controlling the heater current is through-hole soldered onto the PCB. No heat is generated that needs heat sinking, but the solder joints are a weak point. Any weakness in process control during board manufacturer can produce a marginally high resistance joint. Since the voltage is 120 V the high resistance at the joint poses no impediment to the current; the current simply keeps flowing and the joint gets hot. The hot joint starts to oxidize, and gets hotter. Eventually there is a cascade reaction and the joint burns out. When I examined my dishwasher after it failed I found the relay pin was islanded in the middle of the solder cone on the pad and surrounded by a black air gap.
The same thing does not tend to happen with low voltage applications like PC power supplies in spite of the high currents involved. At low voltages a high resistance joint simply reduces the current. At mains voltages the current keeps flowing until failure.
I recognize that many appliances are using this kind of design, but it does not make it a good design. It is merely a symptom of low cost engineering and short service life expectations by the manufacturer.
Design codes for high current mains wiring specify crimped or screwed mechanical connections for a good reason. These are more reliable and durable than soldered connections.
You will do what the job demands of course, but I'm afraid you touched a sore point with me about the quality of design in today's world. No longer are things built to last.