I do agree with your general statement that you can't blame only one cause.
However, peaceful German farmers? I must disagree, Bicicleur...Even Wiki gets it right....they started trying to invade the Empire in the second century
BC, long before the famines brought on by the climate change in the latter days of the Empire. There's an impressive list of battles here, some, to be sure, defensive ones, but many offensive in nature. At a certain point Rome recognized it couldn't absorb new territories, and everything became defensive in nature. As for the last wave of aggression, yes, climate had a hand in it, because of hunger, but also because they were being massacred by the Huns, who were also suffering because of poor grassland.
I do agree that there were periods of internal problems in the Empire, but without the Germanic invasions, propelled by desperation, the Western Empire could have survived, as did the Eastern one. There was also famine in the empire.
See:
https://en.wikipedia.org/wiki/Germanic_Wars
"the general population may not have recovered from the severe plague which struck the empire from 165-180, and likely again in 189.31 J.F. Gilliam convincingly argues that this plague did not kill half of the population as many early historians believed, but he may have gone too far in the other direction by estimating that it killed only 1 to 2 percent of the population. A 7 to 10 percent mortality rate for the empire seems more reasonable.32 Whatever the exact percentage was, it seems clear that this plague disrupted patterns in many archaeological data sets. These data sets show a considerable drop in meat consumption and a decline in the length of the average Roman femur, indicating a shorter and less healthy population. The argument that the climate of Europe at this time was cooler and dryer, if true, would only have contributed to the severity of the plague.33 Based on the evidence available, this plague contributed greatly to the overall population loss which took place during this period. Less than a century later during the worst portion of the Third-Century Crisis from 250 to 270, another large-scale plague struck the Roman Empire, this one starting in the east and spreading quickly, likely due to the movement of soldiers. When this plague is coupled with the widespread barbarian raids of this era it is reasonable to assume that the peasant population dropped substantially. This is especially true when one factors in the scores of slaves and tenant farmers, many of Germanic origin, who would have taken the opportunity presented by the confusion and disruption of this period to flee from their lands and masters.34 It was from this diminished population that the army had to find enough recruits to defend the empire.35"
http://www.kyleharper.net/uncategorized/database-of-pestilence-in-the-roman-empire/
Plagues from the east along with a famine weakened population and invasions spelled the end.
The Germans were by no means peaceful farmers:
"In a victory over the Alamanni by Constantius, Ammianus states the defeated barbarians threw away their armor to run faster, and thus gives a rare mention of Germanic peoples wearing armor.80 In a separate engagement with these same barbarians won by Julian, Ammianus states the Alamanni held the advantage in both strength and height giving a key glimpse into the physical stature likely shared by many Germanic tribes.81 In a description of Persian troops, Ammianus tells us that their military training and discipline, combined with their practice of maneuvers and arms drills made them formidable opponents. They relied heavily upon their cavalry, manned by the nobility, and their regular infantry were armed like Roman gladiators.82"
Many of them had also served in the Roman forces as mercenaries and been rewarded by territory within the Empire. Rome was harboring a fifth column in its midst, sort of like the ethnic Germans in Eastern Europe during World War II".
http://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1577&context=etd
The Eastern Roman Empire handled things in a more ruthless but efficacious way for themselves:they exterminated as many of the Germanic mercenaries as they could manage, and pointed the rest toward the west.
As for Christianity being the cause, that won't wash, although the internal religious disputes didn't help. If it were the cause, then why did the Eastern Empire survive for another 1000 years?
Razib Khan has the following book always high on his list of the ten most important books he's ever read. I wouldn't go that far, but it's very good, and a short read to boot:
"The Fall of Rome and the End of Civilization" by Bryan Ward-Perkins
https://www.goodreads.com/book/show/68540.The_Fall_of_Rome_And_the_End_of_Civilization