Twasn't the case. I pulled out the ancient Hitachi scope to watch the waveform of the tx/rx and ptt signals inside the Signalink USB, its parts easily probed. The Signalink USB is absolved. Does everything correctly. It's cable to the DIN13 is absolved. It's orientation was correct.
Some prior owner of the radio damaged the pins on the jack on the back of the TS-570D. Took a lot of light and the magnifying glass to see the damage. Interrupted circuit turns out to be the nature of the problem. The mic-in + socket is pushed inside the connector housing just far enough that there is no contact.
I will have to disassemble the radio and assess the damage.
Thanks for all who've contributed to motivating me to run down the solution. Ultimately, I might hot wire it, but angers me to do so. Perhaps the solution is to find a parts-only rig and perform surgery. Sigh.
73 Tom W9YW