I finally got the system to work properly. Here's how it worked for me.
First what didn't work: I was unable to get the PCI-e to be detected through any method--I tried a hotfix provided by ASUS, tried installing older versions of the chipset (18.104.22.1681 up through 22.214.171.1240) which all installed fine but still failed to detect the PCI-e root port. Obviously my video card was not being properly detected because it was attached to a port which was not being detected either. I also tried selecting different default video ports in BIOS: iGFX, PCIe, and Auto, and none made any difference. I tried enabling LucidLogix in my BIOS, which also made no difference, and tried installing the LucidLogix Windows driver, which also failed because it detected no eligible hardware.
So I finally just removed the video card and attached one of my two monitors to the motherboard's DVI port in order to run off the HD4000 integrated video chip. Then I tried reinstalling the latest chipset driver, version 126.96.36.1999, which I obtained from the Intel site. And what's strange is, I got the same error the first time I tried it, but after another try or two and a few reboots, it finally detected and worked! I should note for thoroughness that before doing any of this I installed the Intel MEI (Management Engine Interface) which was recommended by ASUS, but I have no idea whether this mattered to the final result because the PCIe device still failed to install several times afterwards and it wasn't until I removed the video card that it worked.
I now had a properly-detected "Xeon(R) processor E3-1200 v2/3rd Gen Core processor PCI Express Root Port - 0151" device in my device manager next to all the other system devices like USB/PCI/etc!
I did not attempt to reinstall the nVidia video card to test whether this worked 100%, because I was intending to eventually switch over to the onboard graphics anyway.
Related note: The onboard HD4000 graphics also failed to be detected for a while after I got the PCIe working, and attempts to install the Intel graphics driver resulted in "computer does not meet minimum requirements" error messages. However, after a handful of reboots, it apparently got detected by Windows 7 automatically, because it found it and installed the HD4000 driver all by itself just when I was about to set the computer on fire and give up. So if your onboard graphics chip isn't being detected, try doing "Scan for Hardware Changes" in Device Manager or running "Update Driver" on it and letting windows search online for the driver.
I hope this helps somebody!