Chip:
I can't help you with the effectiveness of artillery based on range as I don't know of any study of this. Effectiveness would be very hard to determine or calculate as it would be subject to many variables. Variables such as the quality and training of a gun crew, the estimation of range and the cutting of fuses based on that estimated range, quality of the propellent of the charge and other factors. How would you place a value on these intangibles?
As to the various civil war era field guns within a single size, there were different models. Each model had different ballistic characteristics. An example that you used is the 12 pounder field gun and the 12 pounder light field gun, commonly called the Napoleon, both of 4.62" bore. Napoleon was bigger, heavier, longer gun tube, longer range and was well liked by the soldiers. The 12 pounder field howitzer was shorter range, lighter in weight, shorter gun tube but most especially it was older technology, designed for the tactics of the Mexican war and as such became unpopular with the armies and was used less and less. As to the 6 pounder field gun, it had 20 different models in the federal army and had 18 different confederate models. Each of these had different characteristics and it would be impossible to determine effectiveness of so many models when considering the many variables.

Yes, I agree that you should limit of the range you consider for your study to the ranges actually used during the civil war. however, instead of 1,200 yards you mention, I suggest a upper limit of 800 yards because anything over was just not normally used. The 80 yards and less represents 80% of all civil war firing missions. True, many exceptions appear in records, and books but these were not common. In many instances, the terrain and the forrests limited the effective range of artillery firing to these shorter ranges. Remember, that had to see what they were firing at.

Let me suggest that you to limit the information you seek because some of what you seek simply is not available.

Again, I hope this helps you.
Ron