SO... I am <relatively> back in my comfort zone. My stock Sirai Pressurestat is still in place in the machine. When I installed the PID system, I kept it there - just in case I ever ran into trouble with the whiz-bang digital thingamabob.
It took a short amount of time and effort to disconnect the heating element wiring from the PID and re-route it through the Sirai. I now have the thermocouple strapped to the outside of the boiler, and the PID is giving me a constant read from the boiler's surface - not the water inside any longer.
I liked the PID system a lot. By not using it for now, I have an opportunity to read & learn more about the devices and how to program one. This espresso machine was dropped in transit to me <thanks, DHL
> years ago, and the frame is a bit bent. A while back, I picked up another ES-1A on eBay which appears to be <physically> in better shape. I know that it needs a pump rebuild, so when time permits, I will pull the pump & send it off. Once back, I can then test the machine completely, and if it proves a solid machine, I'll look to PID that one, and it should be "the keeper".
I've learned plenty by this dead PID issue. Thanks to you all for your advice & comments. When the rebuild of #2 begins, I'll likely need your collective expertise again!
David