Well, I was approved for an RMA on my Asrock board to my purchaser (thank-you NewEgg). In its place went a Gigabyte GA-Z68XP-UD5.
No UEFI BIOS, no floppy controller, no 2-digit diagnostic LCD.

However, it is clear my new board is built more solidly (not that the Asrock board was bad, just not quite as good), and my Hauppauge HVR-1800 card installs properly, an indicator that Asrock has some BIOS work to do when it comes to properly recognizing PCIe cards, and some additional work to do in ironing out their support procedures, at least in the U.S. Perhaps my problems weren't solved in the way I hoped, but I have solved them now. Unfortunately, Asrock had a chance to really wow me with their Gen3 boards, and came up short. It will be awhile before I try another one.

I guess my summary is that beauty is great, but it can't replace brains (or good cooking).