Why are you avoiding the use of a switch? Surely a switch that can be controlled remotely with the press of a button is much easier than configuring audio outputs in Windows.
I have no experience trying to send video and audio out of separate ports of an AMD card. I have used different video cards to do this (e.g. video from NVIDIA card to display and HDMI audio out of a Core i3-530).
The simplest of all options is to utilize your AVR for all audio requirements.
