OK, I've done more research into the issue.  I started by reinstalling Ubuntu
GNOME 3.10 on my laptop for a clean install, then upgraded to the most
up-to-date packages in Ubuntu's repository.  I have not built any custom
packages.

With this setup, X will not start at all.  Trying to run startx fails with a
segmentation fault and the error:

r600: Unknown chipset 0x9900

This chipID appears to be the 7660G GPU according to this line of the Xorg log:

[ 2200.372] (--) RADEON(0): Chipset: "ARUBA" (ChipID = 0x9900)

Upon looking into the Xorg log, it shows that the 7660G (ARUBA) initializes
acceleration via EXA while the 7730M (VERDE) initializes acceleration via
glamor.  Both cards have acceleration enabled, and then it segfaults before
anything happens on screen.

I want to use glamor acceleration on both cards as I've found it to perform
better than EXA, so I added a simple xorg.conf.d file like so:

Section "Device"
    Identifier "Radeon"
    Option    "AccelMethod"   "glamor"
EndSection

Now X starts, but it's back to my original problem.  With xorg.conf forcing
glamor acceleration, the 7660G GPU initializes EGL and glamor properly which is
reflected by desktop acceleration working, but the 7730M attempts to initialize
EGL and fails, being unusable for DRI PRIME (though still showing up in
listproviders, twice for some reason).

I have a thread on Ubuntu Forums with Xorg.log from both without and with
forcing glamor.  In addition when I tried to replicate the issue on my desktop,
I got graphical corruption.  I'll file a different bug report for that issue.

http://ubuntuforums.org/showthread.php?t=2180826

The conversation that led to this report started here:
http://phoronix.com/forums/showthread.php?84382-RadeonSI-GLAMOR-Support-Still-M-I-A-From-Ubuntu-13-10&p=363236#post363236