I also have a GKK-45. I got it cheap because it kept stovepiping on the previous owner.
I bought some more magazines, but that didn't help. I used White-Out and Magic Marker to see where cartridges were touching. Nothing was obvious. I tried different lubes, and everything else I could think of, short of physical modifications to the gun. Given it was long out of production and spare parts were unobtainium, I didn't want to do something I couldn't reverse.
I noticed its behavior varied a lot between brands of ammo, and the hotter the ammo, the more reliable it was. I broke out the press and made some handloads. It likes .450 SMC loads just fine. It would probably be okay with some of the hotter "defensive" .45 ACP, but I'm too cheap to buy that stuff.
Whatever the problem with mine is must be pretty rare, if not something unique to my particular gun. At least, I haven't found anyone else with a GKK that has had a problem.
The grip is pretty square along the edges and it was uncomfortable to shoot. I got a rubber sleeve from Hogue which took care of the problem.