Fuel for the discussion on both the AAMG and the Finnish StuG with a coaxial MG:
Looking in "Sturm & Drang No.2, StuG III", Japan, 1990, pages 88-89 have three photos of a StuG III Ausf G with a MG-42 in the bracket mount on the top of the shield. The MG-42 has the AA ring sight. Who knows how the crew obtained it, but from a practical standpoint, you've probably got about a 60-degree wide field of fire (for what it's worth, it's better than the 20-degree arc for the main gun

). The same book on page 90 has a photo of a pair of Stug III’s both with a MG-34 on top of the shield with an AA ring sight, and page 112-113 has a large two-page photo of a single StuG also with an AA ring sight configured MG-34.
In the game, as far as the external MG being treated as an AAMG versus BMG, making it an AAMG subjects the crew to being unbuttoned to be able to use it, which would be correct. (I tested that and when buttoned, the shots for the AAMG on a StuG dropped to zero). It also provides use as an AAMG as it seems to have been needed in that role, especially later in the war. To the negative, I believe that in the game as an AAMG it permits 360-degree use, and the code might be generous on the effectiveness. But, treating it as an AAMG would seem to be the reasonable compromise in terms of how the game can handle an unusual arrangement like this.
From a practical standpoint in the game, the only time when the 360-degree capability should be an issue would be if the vehicle was immobilized. Otherwise, the icon swings around to face the target anyway, right? (Although, I just ran a quick test where I immobilized a StuG, and then tried to use area fire selecting the AAMG and it would not fire outside the frontal arc.)
Also noticeable in the page 90 photo is that the mantlet of the first vehicle appears to have the same box-style mantlet with a coaxial MG as the one on the StuG at the Finnish museum, but otherwise does not have the hybrid composition of early and late components. The trailing StuG in the photo appears to have the Topfblende mantlet (Saukopf).
On the deal about coaxial MG, per
http://afvdb.50megs.com/germany/stug3.html “A coaxial machine gun port was added to the welded gun mantlet starting in June 1944, and the cast mantlet in October of that year.” The best example of one of these I’ve found is the one at the Panzermuseum Munster:
http://www.panzermuseum.com/stug-iii...d-vehicle.html Crank up the volume on the video on this page!
Some game relevant features & dates for the StuG III:
Mid Production – September 1943 – August 1944
> Saukopfblend (Cast gun mantlet) fitted to Alkett vehicles (Nov 43)
> Rundumsfeuer (remote controlled MG) mount installed in superstructure roof (Mar 44). Due to shortages of mounts, StuGs produced for several months with armour disc bolted over the hole.
> Nahverteidigungswaffe (Close defence weapon) fitted in superstructure roof (May 44). Due to a shortage of weapons until Oct 44, few Nahverteidigungswaffe fitted, so the hole was covered by an armour disc secured by bolts.
> Block gun mantlet with coaxial MG introduced (June 44)
Late Production – September 1944 – April 1945
> Saukopfblend with coaxial MG introduced (Oct 44)
As a side note, it was not uncommon for older variants returned for repairs to be re-equipped with parts from newer variants creating completely non-standard variants.
Here's something strange... I was using the StuG 276 scenarios 141 thru 147 for testing, and noticed that the StuG's in those scenarios have both the AAMG and a BMG in the game and when you right click on the unit for details. However when you select "Information" it does not show the BMG, just the main gun and the AAMG. Looking though MobHack, the only StuG I saw with a BMG was Unit 873 Stug IIIf.