Your reading of Prussian Artillery is of the 7 Years War and little more. The Berlin Academy of Sciences dated from at least the 1730s and attracted the best minds in Europe to look at the problems of artillery. You have accepted the lead that the Prussians had to the 7 years war. As explained were the problems caused by Frederick the Great taking on the rest of Europe.
The M1768 Dieskau System was advanced and was copied by many nations including Hessen Kassel. This in turn influenced the designs of Hanover, Russia and Desaguliers for Britain. Rightly you have praised the limbers and rolling stock of the RHA.
The material and the training had changed by the time of the French Revolutionary Wars as you so kindly express the consolidation of the training into the Artillery Academy. Before that there was training within each of the Brigades.
Alas please read a little more upon the Canton System and the raising of the artillery train with drivers and horses assigned. They did not use the private contractors that were infamous for the French or British Artillery until the militarisation. Now this was not a permanent establishment as Prussia was too poor. Frederick the Great decided upon a country rather than an army. The army suffered greatly from its peak. The Prussian Army was a fragile construction lacking resources. It was built for limited war and took time to understand the new war. The concept of combined arms and the Brigade structure lasts until the current times.
I find it strange that you had not considered Georg Friedrich von Tempelhoff (1737-1807), and Scharnhorst (1755-1813). Your example predates that of the Seven Years War.
No you are not correct upon the new artillery that was cast from 1809 and rolling stock. It was codified in 1816 when Prussian finally had time to draw breath. This is clear from plans. They 18 calibres long and lighter than the Gribeauval guns that had already been superceded by the AnXI system except in Spain where for logistic reasons this was retained by the French.
Another area that does not seem to have been considered has been the improvement in gunpowder. The better the gunpowder the shorter the gun needs to be. This is very clear when looking at naval guns. It is interesting that the tests carried out by Blomefield that 13 calibres was not inferior to 15, 17 or 22 calibres. As you know well there is a very small payoff in lengthening the barrel to range. The best powder produced for the French Army according to reports came from those in Prussia. The Prussian Army until 1812 had to make do with pre-1806 stocks. Training and organisation is essential for effective use. This was lacking due to the French reparations and occupation. This is explained in my two books on the Prussian Army.
There is still much for me to learn upon the Prussian Napoleonic Artillery as so little is not understood and records are a problem. Surviving examples are problematic due to activities of occupying powers and the USAF/RAF bombing. It is interesting that the Luftwaffe are blamed for lack of reliable information by RAHT.
We have different definitions upon what a System is. Both are valid but I am clear to what I mean. The other part you talk upon is less solid and easy to deal with facts. It becomes opinion based dealing with authors that have invested reasons for their writing. Let us say that we differ. I am at home with the numbers, mechanics and the science.