...I would want to see a capture of the line as it is taken off hook by the system for the good line and the bad line...
Ok, I did that. I can't see a big difference, except that for the "bad" line, as soon as I put the (isolated) scope ground clip on Tip, I get a buzz, which you can see in the trace. I don't know why that happens, and it doesn't happen for the "good" line.
Here's good news on another front: My crazy kludge circuit works! I detect off-hook, quickly isolate the KX-T from the CO for 600 msec, then reconnect them. Dial tone, then dialing/talking works perfectly. A photo of the prototype board is attached. The next step, assuming it keeps working for a while, is to make a little printed circuit board and put it in a small box with two RJ11 connectors.
That may not be as efficient a solution as demanding/begging AT&T for a new line that is different in some way I can't describe, but it sure is a lot more fun for a retired engineer who is in pandemic isolation.
