My first post here, so please excuse my poor writing.
I ran across the topic and found it quite interesting. In fact, I believe I may make a minor contribution to the problems solution.
There are two possible explenations from the german point of view to the british report mentioned above.
The first can be found by anecdotics from turret officers aboard WESTFALEN, who mentions that during the night engagement, some of the british DD´s were approaching below the max. depression his turret would allow. He then makes a description of how he used the ships roll moment to fire off a round at an otherwise impossible angle downwards on a DD at it´s portside.
But I don´t believe this explenation is the one required here because it only explains damage sustained by destroyers in the night action.
For the second idea worth checking I suggest to use informations derived from:
Gröner, Erich: Alle deutschen Kriegsschiffe von 1815- 1936. Unter Benutzung amtlicher Quellen; mit 350 Schiffsskizzen (München 1937).
Note that E. Gröner is proud to base his book on primary sources, only. Some of which have disappeared since due to fires at Kiel destroying the former kaiserl. Marinearchiv in the end of ww2, so his early account is a very important, a valuable source. Make sure You use the revised edition from 1939! It gives some interesting informations regarding the max. range of german 12in armed ships. Page 36 notes that max. range of the 12in turrets from HELGOLAND was 162hm at 13.5 deg elevation while f.e. the max. range of the DERFFLINGER class was 180hm at 13.5 deg elevation.
Note the difference: 18hm (or ca. 2000 yard) at exactly the same 13.5 deg elevation (also confimred by von Hase, the GO of DERFFLINGER in a different account)!
This difference can be traced down to even modern sources. Navweaps online lists a max. range of 162hm at 13.5 deg while Campbell in naval weapons of world war one gives 180hm. Ever wondered about this? So what is the reason for this difference?
This is where Koop and Schmolke helps out:
Koop, Gerhard; Schmolke, Klaus-Peter: Linienschiffe: von der Nassau- zur König-Klasse (Bonn 1999)
The reason for the lower max. range of the Dreadnoughts is explained here by the weaker mounting of the turret design and the gun craddle, thus the 12in HELGOLANDS and KAISERS (except PRINZREGENT LUITPOLDT, which already received the increased elevation gear and stiffened mountings) couldn´t use the same charges as could do the BC´s. This resulted in lower muzzle velocity, corresponding lower range and a steeper angle of fall at this range.
All of these issues were adressed when the ships also received their increased elevation gear after Jutland.
Unfortunately, I cannot comment on how this was practicised but either they dismissed off the fore charge bag (thus the brass cartridge was the main and only charge) or they used special brass cartridges with lower powder content. Anyway this difference is systematic and related to different turret designs and was not something like an "option" the gunnery officer could make use when he think it fit´s best the tactical environment.
Judging from the battle distances in the run-to-the-north, some work on the mounting was done before the battle (probably- but this is a speculation on my part, in response to the need for increased range due to experiences from Doggerbank). Evidently the ships of the KÖNIG class and SMS KAISER + SMS PRINZREGENT LUITPOLDT weren´t affected by the mounting issue (or else You cannot explain why they opened fire and hit targets beyond their respsective firing range as none of the firings was done at distances closer than 18,000 yard in this part of the battle).
Hope this helps,