I still have to respectfully disagree about the number of Hits being a poor measure of firing accuracy. Theoretically if all the known variables are accounted for, we would not need a probability model at all. We would know all the variables, and would achieve a hit with every shot. However the more unknown variables there are, the less we know about the problem, and therefore try to compensate for this by using innaccurate mathematics which we call "probability". The more that the unknown variables can be reduced, the greater the certainty of achieving the intended outcome.
Applying this theory to the gunnery problem, the more accurate the information on the target, the higher the chance of achieving a hit. Therefore, despite what you describe a hit as a random event, in fact it is not a random event, its just an event that cannot be predicted with the tools at hand. However if the tools at hand are made more accurate, then the "Unknownness" (which you call randomness) of the hit event drops, until at some point it is not really an unknown variable anymore
Now the question is this, were the tools available during the war capable of eliminating a hit as an unknown outcome. I dont think they were, because in the post war environment, with superior methods and technology we still could not eliminate the randomness of achieving a hit. This part accords to what you are saying...
However the chances of achieving a hit can be increased, if the accuracy and precision of those tools can be improved. You mentioned the circumstances of the Eckoldts loss, which is very true (though I believe she was still some thousands of yards away from the british Cruisers when lost....her consort beitzen did escape....if it had beeen an 1880s style engagement, it was unlikley the beitzen would escape), nevertheless this was still part of the probability matrix for a successful hit for wwii gunnery....its just that the probability of a hit in those circumstances was so close to one, as to effectively render a hit at those ranges a certainty. At longer ranges the same could be achieved if the techniques the training and/or the technology could be improved so as to also increase that prob to 1.
So what are the ingredients that can improve the probability of a hit. This is obviously a matter of opinion, but my belief is that the main elements in the probability matrix are not limited to those you mentioned, they include....
1) The standard of crew training if human errors creep into any part of the operation, this would have an overwhelming effect
2) The speed that target data can be transferred from the point of data collection to the wepons platforms
3) The size speed and manouverability of the target
4) The target range
5) The visibility of the target This is where radar has its greatest effect
6) The sea state and the stability of the firing platform
7) The inherent accuracy of the guns firing
etc etc
My belief is that inherently in the latter part of the war, the British were more accurate than the Germans in their gunnery. I am sceptical that the Germans held some sort of technological advantage over their opponents, but even if they did, this is just one part of the equation. maybe, for example, German ships were less stable than the British counterparts, or their gunnery crews lacked proper training at the end of the war. I dont believe, however, that the Germans possessed as great a chance of hitting a target in the latter part of the war as their allied counterparts. Thats an opinion, its open to debate and disagreement of course