I have found the answer to my problem. nVidia's GeForce 8800 GT might be stated to be Mac compatible, and even was a build option in earlier Mac Pros but user-purchased models will suffer problems after a time, at least on the early 2009 4,1 model. I have come to this conclusion as I decided to try using a second-hand example of the GT120 originally specified for the 4,1. One, may it be noted, that was taken from another Mac Pro and was installed by Apple originally.
My machine is now purring like a kitten.
Another suggestion is that you might have to find your own answers... It seems that some people simply don't have the good grace to be bothered enough to read your description of your problem properly, or take your own knowledge seriously, and they can waste your time...