I would just use the one in the Elric core rules, because Moorcokc doesn't usually give exact dates. Chaosium's Stormbringer books give similar time line and their Atlas of the Young Kingdoms gives more detailed time lines for kingdoms of the Northern Continent around the time of Elric (although the book isn't 100% compatible with Mongoose's Elric material).
Personally I wouldn't worry too much about the timeline. My own campaign started from the last years of Emperor Sadric LXXXVI, so that the possibility of comign doom doesn't interfere too much with the campaign. In general, while I occasionally like to use Moorcock's characters like Jhary-a-Conel, Philander Groot or Klosterheim*, I like to keep events of the Elric saga in background and I don't want to make players as part of Elric's doomed quest.
*So far I have used Philander Groot only in Mittelmarch adventure (which was based on "The War Hound and the World's Pain" by Michael Moorcock) which my regular Elric players played with different characters. Klosterheim I have used in both Young Kingdoms and Mittelmarch settings, although his incarnations were quite different.
