You're spot on. The DGA-M is the long action. I haven't measured to see if you could fit a magnum length cartridge (such as a .375 H&H) but I have seen one such Shilen rifle advertised for sale. I can tell you that it fits a 25-06 with plenty of room to spare. From my experience, the DGA-M also has a blind magazine making it a repeater. Personally, I haven't run into a regular length action that is a repeater but that doesn't mean that they weren't made and I can't say that all DGA-M rifles were repeaters. Again, I'm just going from what I've personally seen.
Here in the States, I see them advertised fairly often. I've limited my collection to those with octagonal barrels. Both in my collection are what I would characterize as "medium heavy" contour.
I try to keep my eyes open for rifles that fit what I collect and I've noticed your posts on forum.robsoft when I run my google searches. Its good to see that the sport is alive in other parts of the world.
When you say your rifle is a .222, I assume that would be .222 Remington?