Sorry I can't help with you question, but as for the "unuseful" PID there have been a few people who have converted them to SSR output as I think the control circuit to the internal mech relay is the correct voltage for a SSR, basically as it would go in my head it was open it up - desolder the relay - solder jumers from where the relay control pins were to where the output pins were - close it up and away you go.... And, he did not want the other one back, so I have it. Though I have no use for it.
Do a search on here first though cause I might be wrong