I had the exact same problem, misfiring in all cylinders though. Yea, that violent shake is the MAF attempting to send signals but instead of the on off signals it normally sends, its a flat line. I experienced the violent shaking in my jetta when my MAF went bad, and in my old Toyota Land Cruiser.

Take off your stock one make sure its not dirty, and since you have it off, clean it with rubbing alcohol or i was told carb cleaner is just as good, just dont do what I did and DONT USE WATER!!! also when you take it out see if any water drips from it, if you find that, their is your culprit