If I am correct, resolutions about 1680x1050 is put into the "HDTV" category. So selecting 1080p under "HDTV" is okay. In fact, that is the setting I am using for my two monitors.
The black border can be removed by simply adjusting the Under-Scan / Over-Scan option within CCC. It is located in "My Digital Flat-Panels" >> "Scaling Options (Digital Flat-Panel)". Move the slider to 0% or to the Over-Scan end.
Did you mess with any of the settings under "My Digital Flat-Panels" >> "Properties (Digital Flat-Panel)"? Try unchecking the "Enable GPU Scaling" box, and make the "Enable ITC Processing" box selected.
I realize you mentioned the Scaling Option is grey-out, but set it 1080p and give it another try.
You are not 100% guaranteed that an ASUS Graphics card should work with an ASUS monitor. Besides, the Core component (the actualy GPU chip) is made through AMD, not ASUS.
FX-8350 @ 4.8GHz // ASUS Crosshair V Formula 990FX // Sapphire Vapor-X HD 7970 + Dual-X HD 7970 // Thermaltake Frio w/ push-pull (using Antec Formula 7 Nano-Diamond + Cooler Master JetFlo fans) // 8GB (2 X 4GB) G.Skill RipJawsX 2133MHz // Corsair TX850 850W // Corsair Force GT 120GB SSD (OS) // Kingston V200+ 120GB SSD // WD Caviar Black 1TB // Windows 7 Ult x64