Do NOT kill the play for this forward motion. Suppose the player stops for a full second? Or suppose he changes direction and moves latterally along the line?
It's not a foul to move forward, it's a foul to be moving forward when the ball is snapped. If the player can cure his "error" before the snap, then he has to have that chance.
That being said, there is a difference between moving forward at the snap, and moving forward SIMULATING the snap. The latter foul is a false start and shuts down the play.