I have a Weber 120, Serial number AD0574138, following your instructions from the start of this conversation, I bought your suggested parts using your hyperlinks, with the exception of the hose, now not available.
My situation is that the On-Off Valve, which is screwed into the defective regulator, does not use a 1/8" thread pattern. I took the valve to a couple of nearby hardware stores and was unable to determine what the thread pattern is on the gas examples, since no one nearby has metric gas fittings (metric is my guess).
Do you have any suggestions on where or how I should look for the proper parts for this conversion?
Bruce, I really appreciate the thoroughness of your initial posting.