Hi RK,
Don't get me wrong, I think you're on the right track. There's little or no doubt about the GMSG / DDR link. The pistol has many hallmarks of a normal 'VoPo' rework and might have been issued to some sort of company security force, although it's not impossible that GMSG had something to do with the refurbishing.
But, in the DDR they used a 'lieferantnummer' or manufacturer's code similar to the nazi-style. The DDR codes were 4-digit numbers, 1001 being a wellknown one, representing the former Haenel works. The Haenel works didn't mark or stamp the pistols they refurbished with a maker's code, only newly manufactured magazines had the code.
It would be nice if GMSG had code 1191

, but sadly I haven't been able to find DDR code lists yet.
Basically we have two options, both valid until more proof surfaces:
-GMSG is refurbishers mark.
-GMSG is a property mark.
Unquestionably, the pistol has a DDR background.