EspressoParts sells a kit that replaces various parts; is there another way of doing it that doesn't involve so many changed parts?
The short answer is no. EPNW has done a very admirable job of putting together a turn-key kit to upgrade the LM Linea brew boiler temperature control. Why not buy the kit from them less the parts you have "laying around"? The thermocouple adaptor they supply is unique (AFAIK) because it has 1/2"-14 BSPP threads and accepts a 1/8" thermocouple. That size combination is rare - certainly available as a special order (6-8 weeks) from Swagelok but EPNW has it in stock.
As regards the steam boiler, I sorta understand your desire to get rid of the "clack-clack". So, why not apply a less expensive Pstat (LM appears to use CEME's on their GB-5) and a suitable solid state relay? Yes, I have read and do understand where heating element life can be prolonged with PID control but that can be an expensive life extension project. But, if you insist

, the fitting for the existing pstat is probably 1/4"-19 BSPP and Swagelok adaptors are readily available to fit that port and accept a 1/8" thermocouple. The correct Swagelok P/N for a 1/8" thermocouple and that size port would be B-200-1-4RPBT. "BT" stands for bored-through and you need that type of fitting to pass the thermocouple.