The fire three broadsides from pistol range & board in the smoke mentality of RN captains did not allow for general adoption of such a rational system.
So something that I thought might be helpful was that, in the past, I've seen the regulations for gunnery in the US and British service at the time in question.
Here's an excerpt from the British one.
'Men in Sea-going ships are to be encouraged to qualify themselves for "Acting Captain of Gun" under the instruction of the Gunnery Officer, in which case they need only be required to be perfect in the first
three instructions, but each man before receiving his certificate must have fired at least the following number of rounds, and have proved that he can lay a gun quickly, and is a good and efficient shot:-
120 rounds from a rifle at objects distant from 200 to 800 yards...
20 rounds from a revolver pistol
30 rounds from a 6-pounder short practice gun, half being with motion
10 rounds from a great gun, half being with motion
On their arrival in England to pay off, they must pass through one of the Gunnery Ships to be confirmed in their present certificate, or to qualify for a higher grade.'
(
Instructions for the exercise and service of great guns, etc., on board her majesty's ships, 1858)
The same manual gives instructions for how to use Moorsom's Director, which means that it was at the very least official equipment.
What this means is that a gun captain in British service has experience at estimating range, and dealing with both practice guns and big guns including firing at motion. Moorsom's Director is official equipment.
And here's from the US one (
1860 manual).
279. Officers of divisions and Captains of guns should be occasionally practised in measuring the distances of objects by the eye, at times when opportunities offer of verifying the accuracy of their estimate by compar- ing it with the distance obtained by the foregoing methods, or any other which will afford the best means of comparison.
No official requirement for qualification or training.
This set of regulations also touches on the idea of combined fire from many guns, and specifically it says:
292. Concentration of fire may be desirable under certain circum- stances ; and arrangements have been sometimes made to secure it by the simultaneous discharge of a number of guns upon some part of an object whose distance is known.
The advantages of these arrangements are not very obvious, excepting in cases where the position of the enemy may be visible from one part of a ship and not from all the guns in the batteries. Even in these cases, however, it requires that all the guns which are to fire in this manner should be regulated by one gun, and all be fired at the same time, which it would be difficult to accomplish ; and, if successful, the simultaneous discharge from many heavy guns may be considered objectionable.
Concentration of fire upon a particular part of an enemy's vessel may be obtained by a general order for the guns to be aimed to strike that part, leaving the Captains of guns to determine the proper time for firing, according to circumstances at the moment. This obviates the objections due to simultaneous firing and would generally be equally effective. In this, as in all other cases at sea, success would depend mainly upon the skill, judgment, and coolness of the Captains of the guns.
In other words, the USN's official opinion on coordinated broadsides under central control was "don't do it".
The 1864 one added that gun captains should be examined by the surgeon with respect to eyesight, but added no qualification requirements.
One of these services is paying greater attention than the other to the cultivation of the skills required for accurate long range fire.