Re: The chances of it discriminating accurately between 535 and 541
The 535 event is intriguing because it is even larger in magnitude and area than the 1816 'Year without a summer' caused by Mount Tambora. Reports of incredibly cold winters, crop failure and dry sulfurous fogs extend from Northern Europe to China, the Middle East and South America.
A volcano is the most likely cause, but one at high latitudes (such as those in Iceland) would be unlikely to affect the Southern Hemisphere, so efforts have previously concentrated on suitably monstrous mountains in the tropics including Rabaul (New Guinea (erupting right now)) and Lake Ilopango (El Salvador). To cause the drop in temperatures it would have to be a VEI 7 eruption - think ten Pinatubos or one-thousand Eyjafjallajökulls. Last year there was also a suggestion it might have been caused by a devastating, eruption of Krakatau previously dated to 416 from Javanese historical records. There is however little geological evidence at Krakatau of an eruption in the mid-6th Century.
Going back to Iceland, if they can find a sulfur spike in a core from the Greenland cap (which can be pretty easily dated to individual years) which has a sulfur isotope imbalance they can ascribe it to a large event in Iceland at a fixed time. Most Icelandic eruptions don't inject much sulfur into the stratosphere, so for the isotopes to be buggered it would have to be a big one along the lines of the VEI 6 Eldgjá and Laki eruptions of 934 and 1783 respectively - neither of which did much good to the environment.