Alright, after following what Dyre Straits said I'm back at 10.4. I didn't go exactly like he said, but I'm on 10.4 an all my monitors are working well. I'm a bit afraid to attempt going to 10.9. Are there any real benefits to updating? I may just stay here since everything is working.
What step did you not follow "exactly"? I tried to be very, very specific in how to do this correctly. I've been using ATI cards since 1996 and very rarely ever have had driver update problems.
Be that as it may, there is a Hotfix 10.9a driver set released that I believe you should try. It's a much larger download and may be the fix you need to get 10.9 installed correctly. I'm using this set now. Ignore any notes that these are "only for some HD4xxx" cards. The longer release notes indicate other fixes as well. Follow my previous advice to get back to your 10.4 drivers and then WITHOUT UNINSTALLING 10.4 just run the Install option. Don't uninstall anything.
Here's the link to 10.9a Hotfix: http://support.amd.com/us/kbarticles/Pages/ATICatalyst109Hotfix.aspx
There is one further note about these: They are not WHQL certified. The only thing you really need to know is that, when you get a warning prompt during the installation, just click on Install Anyway. VERY IMPORTANT! All this warning is telling you is that Microsoft has not issued certification for the drivers yet. That's it. These will not blow up your PC. ;)
Good luck!
EDIT: Just one other note: Have you checked with ASUS as to whether there are updated drivers for your MOTHERBOARD? This is just as important as updating any other drivers. So, check with ASUS as to whether there are newer system/motherboard/chipset drivers.