Major update on my issue....
I took the TT cable and the new one to an "old time" electronics store in my town, one run by a couple of long time ham radio guys. It is a one-of-a-kind business for sure...everything electronic, and I don't mean the electronics department of a big box store.
Anyway, I asked them to take the plug off the new one and put it on the TT cable, and showed them the video from above. He looked at the cables awhile then started into it, cutting, dismantling, de-soldering...
then picked up the plugs, some pliers, unscrewed the tip end off the new cable plug and screwed it onto the old one. That was all that was needed. The cutting and dismantling was unnecessary, but had been started. So he re-soldered the wires back onto the circuit board in the original plug and reassembled the plug. About an hour of bench work for what could have been a 30 second, no-cut fix. But since he didn't discover it, he only charged $10 total.