So you're saying that the political situation in Rome was not the cause of the economic and population decline (and other disruptions), but simply coincided in time with the climate change that was the actual cause?
Since the Dark Ages happened many decades AFTER the German takeover, they are not connected.
A Fimbulwinter is not exactly a climate change ~ it's just an adverse winter weather pattern that lasts beyond one season. Things always return to normal!
Of course, that one was bad enough that everything got eaten and then they burned everything down to keep warm. When the Bretons arrived in France from Great Brittain in the 7th Century they observed that there were no people and few animals. In fact, it is claimed that the great magician Merlin had to replant all the grapevines in Beaujolais! The Carvajal clan penetrated all the way to the Jura mountains without encountering any other people. Obviously the invading barbarians had been destroyed by this disaster. In due course Ireland became the center of Christian thought, action and missionary work for Western Europe.
Hope y'all don't mind me putting about 11/2 cents in.
There was a mini-ice age around 1100 AD. Not sure of the dates, but it was probably caused by an astroid crash or volcano. There have been several TV shows on it. The effects were noted in civilizations all over the world and the rings of trees from different locales bear the theory out.