I ordered some digisparks from ebay, and a packet of ball-tilt switches.

From the HID reference, I'm going to try using F23 and F24 to signal position 1 and 2 respectively (depending the the orientation of the monitor's USB ports, that might be portrait/landscape or landscape/portrait): http://www.usb.org/developers/hidpage/Hut1_12v2.pdf

I also found an existing digispark example for a V-USB based keyboard.

And finally, a C# gist for the actual screen rotation part: https://gist.github.com/umq/986635

Hopefully this can be a short project!