You have installed the drivers, you just don't have your display configured the way you'd like. Sounds like a display detection issue, which means it's a windows problem.
I was having a similar issue a while back, and Calamity linked me to this - http://forum.arcadecontrols.com/index.php/topic,143136.msg1484489.html#msg1484489
You used to be able to get windows to detect a display by adding a 75R termination to one of the colour lines of the VGA port (R,G,B). I think you still can. As in, a 75 Ohm resistor between the signal line and ground. Does the Audio Authority unit have a 75R termination? When you plug it in, does it come up in Windows, but without a name and just as a generic non-pnp monitor? If not, if you have to manually force detection, windows does not detect a display on that port and defaults to the other port as the primary once you unplug the LCD, or simply filters out the mode you're using as unsafe. First, I'd try things as normal but swap which monitor is plugged into which port. If that doesn't help, and you're not happy building something to terminate and stay in the line, you could try unplugging the Audio Authority and using a 75R resistor directly in the VGA port (make sure you get the right pins though!) then unplug the LCD like that, wait a second, then remove the resistor and plug the Audio Authority back in. Probably won't work either, but worth a shot.
If the Audio Authority comes up in windows with it's own name, not just as a generic non-pnp monitor, then it has it's own EDID. And that's a problem. You'd need to remove or blank that EDID, possibly ruining the unit, or, and this way works better than any of the above, simply use a 5000/6000/7000 series Radeon card instead, so you can take advantage of the EDID emulation they offer with crt_emudriver. That always works.