I have the older Vaio Z with the 9300m GS and I have this same problem, after I install the drivers only video out (VGA/HDMI) works and QE/CI does work, but the internal monitor is not detected and stays blank.

The only way to get anything on the internal display is to remove the drivers. On the Intel it is possible to get the proper resolution using Chameleon and the Graphics Mode option but still no QE/CI, I have not figured out how to get the proper resolution on the nVidia at all.

There are proper drivers for both sides on Ubuntu using the Sony-VGN-Zseries-janitor script, but it still only supports cold switching (have to reboot to switch the GPU), maybe this could somehow be ported to OSX.