It didn't take long after re-reading my post to see that I had it upside down. That's why I had CAN-H and CAN-L where RXP and RXM should have been. I should have trusted my initial instinct, which was that feeding a CAN signal into an Ethernet adapter was weird.
I built my adapter based on this image.
To my eye, this seemed as if the narrow side of the connector was at the bottom of the image.
However, comparing to this image, the error of my ways was pretty evident.
Anyway, long story short, I corrected my adapter and gave it another try. I needed to add a firewall rule specifically for network_configuration.exe, and execute that directly as Administrator to get the adapter configured in Vehicle Mode.
I've got the green indicator of success.