The reason why every source is more argument than narrative is that every single aspect of the narrative for this particular chapter of history is ferociously contested. The dating is contested, the size of the invasions is contested, the Roman response to the invaders is contested, the degree of social upheaval is contested, the ethnicity of the invaders is contested (oh Lord how its contested) and so on and so forth. So bearing in mind that any narrative is also an argument, you might check out:

Peter Heather's 2005 book The Fall of the Roman Empire is eminently readable and, as I recall, fairly chronological. As the title suggest though, he is part of the camp that views the barbarian invasions as destructive and largely responsible for the collapse of the empire in the west.

Walter Goffart is perhaps the most notable member of the other camp. His 1980 Barbarians and Romans, attempted to show how the Romans rather peaceably accommodated barbarians by granting them the right to collect taxes from certain lands in exchange for military service. More recently he wrote an article in History Compass (2008), “Rome’s Final Conquest: the Barbarians," which would probably be of more interest to you because it has a lengthy timeline of important events compiled by an advocate for accommodation. It therefore pairs well with Heather's book.