I think that theonlyrealbeef once got a 5 turn EM win versus hermes.
Indeed, Hermes' damage is fast, so it can be countered fast as well

Dragoon1140 also once claimed a 4-turn win against Octane with Voodoo, not sure if it's true though :p (wouldn't be his first prank

) Or if it was an EM for that matter.
Edit: proof of a 4 turn EM vs Gemini.

(
http://imageplay.net/)
Looking at quanta I can see I lost coin toss since I drew 12 cards during these turns, and used 0 Precognitions:
- turn, play Entropy Pendulum end of turn: 2
, pendulum shows 
- turn, still 2
, pendulum shows
- turn, 3
, pendulum shows 
- turn, 3
, pendulum shows
, TU for the win (see Screenshot)