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"The spacing intervals between firing were so long that the natural roll of the ship in any sort of sea would disperse the shells and I don't believe that the FC would correct individual guns to take account of this."

The technique of "continuous aim" involves the gun layer holding the target ship in his sight and adjusting the elevation as the ship roles and pitches, so that the gun is continuously held on target. It was invented around 1898 by Percy Scott, who adopted a methods and apraratus for training gunlayers and trainers to use the technique. The effect of its introduction in the Royal Navy improved the results of hand work QF guns battle practice firings at 1500 yards from 30% to nearly 70% hits. By 1905 most RN handwork guns were aimed this way.

Its introduction to heavy, power worked guns was limited by the reliability, power and accuracy of the turret machinery. The Royal Navy introduced improved "swash plate" motors to allow continuous aim and backfitted them through the fleet after 1910, though the hydraulic power required continued to strain older ships.

Director firing maintained this principle.

Later on (1920's+?), it was found that roll accelerations at different periods in the roll introduced small errors, and procedures were changed to continuously aim but to fire on the roll, and various modifications were made, including a gyro to automatically fire at a certain point in the roll. Note though, that 1930's RN handbooks treat this as optional, and a wide range of firing options were open to a WWII RN gunnery officer, apart from gyro firing.

So yes a 1940's fire control system should be able to account for firing a small salvoes a few seconds apart at different periods in the roll, though this mode of firing may not produce the most accurate shooting that any given ship is capable of.

Good references for this include.

Peter Padfield "Guns at Sea" - old but excellent explation of the introduction of continuous aim, including diagrams.

Brooks "Dreadnought Gunnery and the battle of Jutland" - more on continuous aim for power worked mountings.

RN gunnery handbook - on line at the Hood site I believe, excellent for gyro firing etc and other role corrections.

Norman Friedmans new book on naval gunnery is due for release within the next month, and I have pre ordered my new copy.