I think you may be misinterpreting the cause and effect...
The effect is that your site dropped, but I doubt the cause was due to a EMD. It was probably due to 'over-optimization' - when you were backlinking, did you vary your anchors between naked links, generic words, and target keywords (with the least focus on target keywords)?
Chances are, you were targeting that particular keyword which the EMD was for, and therefore are serving a penalty due to over-optimization and an 'unnatural' backlink profile.
Hope that helps?