FIXED! (I'm posting this to hopefully help anyone else facing this issue).
I did some more digging in this forum and found a reference to the "Kinect Monitor" service.
I checked in services.msc and sure enough it was not running. I reset the service to auto-start and manually started it - which did not fix the issue when using the SIIG PCIe USB3 card.
The Kinect V2 Configuration Verifier tool gained one more step - clearing the "Verify Kinect Software Installed", however the frame rate was flaky - 1 to 2 frames per second - so the final verification step failed. Getting closer but not there
yet...
However, when I plugged the Kinect back into the USB3 port on the motherboard everything worked (Intel i7/c216 USB chipset).
So before spending money on a new USB card, check that the Kinect Monitor service is running.
On my setup, the keyboard and mouse are on the motherboard's USB2 buss, the Kinect is the only device on the USB3 buss, which seems to be working fine.