If you go to http://kernel.org/ and look for a "stable" kernel, you get 3.7.3. Not supporting it is not the right thing to do.
I run Debian Testing and i have the 3.7.3-trunk-686 kernel installed from the experimental repos. Today i installed the 13.1 driver from the experimental repos and works perfectly (installed for both 3.6 and 3.7 kernels), so they probably patched it already it seems.
Previously the 12.11 driver wasnt compiling on 3.7 unless i applied the patch.
Debian added the 3.7 patch for -1, if you get -2 then it should contain the 3.8 patch as well.
As a new Windows Legacy Catalyst is available
Windows Legacy Catalyst 13.1
I just checked the Linux driver page and there is also a new one listed as Catalyst 13.1
Linux Legacy Catalyst 13.1
Contrary to the Windows driver, the version on the top of the page still says "Version 12.6" but is called "Revision number 13.1".
Apparently the driver is still stuck to kernel 3.4 and X.Org 1.12.
Overall 13.1 from the Debian repo is working quite well for me (except that amdcccle could not handle my multi-monitor configuration and I had to set everything in xorg.conf.)
But when I just ran Unigine Heaven 3.0 via the PTS I got horrible tearing and flickering. At any time the main screen is about half black and half rendered. Does anybody have an idea what could cause this? The Vsync option in amdcccle didn't change anything.