"The Dark Ages were caused by successive waves of Teutonic invasion"
Wrong. Ask Hypatia...
Unluckily, the Edict of Thessalonica started the attempt of the christian bishops to attain political power using religion violently against opponents - look at what Cyril made in Alexandria, and it wasn't because of the Huns (although his Parabalani were not much kinder)
And some "barbarians" - look at Theodoric or Frederick II - were less barbaric than many popes, which obviously worked hard to crush them because they could take the power away from them.