Ok, the last setting where the Core frequency was set to 150 and Memory to 125 worked only for some apps. When playing Airstrike 3D, the artifacts reappeared. Another utility was used to find an alternate solution to this problem and maybe it’s the definite solution here.
A utility called ATI Tray Tools v184.108.40.2060 was used to alter the GPU core and memory frequencies. Below is a screenshot of the utility and the settings used.
I moved the two sliders all the way to the left and then I set the "Restrict reference divider up to" value was set to “4”. Then I hit the "Calculate" button. This caused the utility to calculate the most appropriate values for both Core Speed and Memory Speed. So far, these settings have worked well with the Sach’s Aquarium 3D Screensaver and my Airstrike 3D game. Before, one of these two apps always showed up with artifacts within 5-10 minutes of use. A couple of hours into game playing and so on with these new settings has still not produced any artifacts. These settings are working very well for me and I was wondering if anybody else can try these settings to see what they get, unless you've already tried them. I've yet to continue testing these setting so I'll keep y'all informed. Right now, these settings provide a system that is very usable although maybe not the optimum but hey, at least it's much better than what I had before.