Battery D of most artillery battalions is the service battery. That is the rear echelon supply and support troops. It consists of the following: Bty HQ and HQ section AM&S section Maintenance section Admin and Personnel section Battalion maintenance platoon Battalion supply and transportation platoon
I think you are tinking of Head Quarters Battery , Head Quarters & Head Quarters Battery or Head Quarters & Service Battery. I have never seen a 'Lettered" unit be anything other than a 'Line' unit. All of the examples you give are things that would be organic to a HQ BTRY, H&H BTRY or H&S Battery..........you need to think of a 'Battery' being the same as a 'Company' in a line Battalion. The other thing to consider is why would 'Guns' be allocated to a battery if the primary job of the personell in that Battery was not firing the guns? Each Battery also has it's own Headquarters section usually less than a dozen guys.
You could; but, it's your research and your decision to make. In the first diagram you posted it is labled as a 'Battery'. What is the purpose of you diagram?
I'm doing the diagram for fun and for a better understanding of how units in the 85th Division were organized. For me it's easier if I can visualize it in diagram form. I renamed the HQ and Service units as Batteries so I think I'm satisfied with the diagram unless somebody sees anything else that needs correcting.