Well, I tried a combination of your suggestions & added a little hair spray (yes, hair spray) and I seem to have a fix.
I cut the Z bend off the engine end of the cable & pulled the lower half of the cable jacket off.
I then cut about 1/2" off the lower half. I cut about 3" of plastic tubing I had left over from installing a dishwasher (I think).
Then I cleaned the upper, lower & tube with methyl hydrate. Next, I put the tube over the inner wire until it was close to the upper half. I then hair sprayed the upper cable & shoved the tube up as far as it would go. I then trimmed the tube so I had about the same amount below the break as above the break.
Hair sprayed the lower half and shoved quickly (it dries fast). The hair spray is slick as snot while it is wet and sticky when dry. (My motorcycle friend gave me that tip for putting grips on handlebars.) I then reinstalled the cable & remade the Z bend. Works fine ... so far.