It worked!! You are a god!!
Here's the card that worked for me:
https://www.amazon.com/gp/product/B00FPIMICA/
It has 7 ports, 5 outside, 2 inside. Pretty cool plugging in flash drives *inside* the case!
The device is installed and detected as "Fresco Logic", per the software.
No BSODs, no forgetting-the-device-install, works flawless. I rebooted about 10x just to be sure, unplugging and re-plugging.
The cards that did *not* work are the VIA 805 and Renesas units. 3 of them.
Thanks again!