From a 10.2.6 factory install, I used bin4ry's root script - took a few goes to get it going right (installed SDK and plugged in, device showed as "Kindle"; then installed Kindle HD ADB driver and device shows up as Android Composite ADB Device) and I had to kill the adb.exe process which the SDK installed and had running in the background. I DIDN'T need to elevate UAC privileges; indeed if I did that I just got path errors with the script. Local user privileges are all it needs, it seems.
I then used the cordless (wireless) APK install method, I thought it hadn't worked as the device booted, but I kept on seeing brief flashes of the Kindle bootscreen on top of the UI (which did respond, although very laggily). Seems this was just part of the rooting though as I left it for a minute or two and eventually the MS-DOS prompt reported success. The KF2 rebooted, and I got the blue logo bootscreen as expected. The device then booted into stock ROM perfectly.
My PC then took a little bit longer than usual for the device to show up again as an Android Composite ADB device, but it did happen eventually (a couple of minutes after booting).