Wow how odd. Have you done a game reinstall? It does sound like something could be up with your version of the game considering everything else looks alright. (retail? digital?) If you do go ahead with a reinstall, after uninstall run through with ccleaner then reinstall. (have the saves backed up!

Have you checked the cables for your ASUS? As in, any of them bent or damaged which could interrupt the data flow? I'd also suggest unplugging them and giving a quick blow to remove any dust
Any device updates for the ASUS? As it's a 24', does putting it up to 1920x1200 change anything?
Device Manager > PnP Monitor >Update driver
Alternatively, do you think this fix could work for you?
http://www.tomshardware.com/forum/346844-33-black-screen-screen-tearing-radeon-6870#t2594132
sorry i can't help anymore

i'm not with my computer right now to compare, although you have better specs so I'm not sure why stuttering on you
