This is an awesome post, great work!
I am in the process of building a very simple electric kettle as well. I am going to wire 230VAC to a 2-pole contactor (120VAC coil), then run the other side of that contactor to my heating element. I will punch a hole in my 8 gallon pot, and insert the heating element through there. Then, I will install a simple temperature controller ($15 on amazon) that runs on 120VAC. When its temperature probe detects water colder than my desired setting, it will close a relay, which will output 120VAC to the coil of the contactor. Not quite PID, its just a matter of "water too cold? turn on heater until the water is hot enough".
I am an electrical engineer and work in industrial controls, so one day I will write my own software and get industrial grade controllers to do all of this. I plan on integrating a touch screen as well, so it will be very cool. For now, I just plan on using the above setup. All I want is the ability to bring my 7 gallons of wort to a boil indoors, the simple system should do the trick.