First, thanks everyone for your advice. Things are working fine!
Here is my shopping list:
I bought the RTD because I liked the size, and it was readily in stock. The sheath is only 50mm (a couple of inches) and this makes placement inside the kettle simple. I just have it hanging in there now, but will come up with a way to hold it in place just above the screen as suggested earlier.
Since this system is to provide 110VAC to the La Peppina it is wired differently than many of the examples you might see for espresso machines in which a thermostat is replaced. An SSR is an electrically activated relay, so connecting the output side of the SSR to a socket and plugging in the La Peppina is not going to do anything for you (sorry if this is obvious, I was scratching my head when looking at wiring diagrams where there was obviously no 110VAC source for the controlled device).
I have been testing today with using the 220VAC 700W La Peppina plugged into 110VAC. With water starting out at 65 degrees F it takes 45 minutes to get to 199 degrees F. This is fine for me as I do not generally rush around, and if I need a faster warm up I can always heat water in my 1500W electric kettle.
At this point I would say that this has been a fun project and I will surely learn quite a bit about making espresso. Regarding cost: It was slightly cheaper to build than purchasing ready made, and building forced me to learn a little more than I would have.
Time for a shot (of decaf),