One of the items in the Line of Scrimmage section of the Philosophies states that:
"When in question regarding player position on movement by the defense into the neutral zone which causes the offense to move, a [defensive] player is moving toward the offensive player. This protects both that [offensive] player and the two adjacent offensive players."
If he gets into the NZ, the idea is to try to make him heading for an offensive player, so that the maximum number of offensive players are covered by the 'reaction' rule; if those three react to the defensive player's movement, they are NOT guilty of a false start. In your secenario, the gap would need to be very wide, and the defensive player clearly moves straight ahead. That would be rare. "Stretch" this into a defensive foul whenever possible.
Make note of the new philosophy that does not require the defensive player to actually penetrate the NZ. If he is moveing toward the NZ and causes a reaction by the appropriate lineman (linemen), make it DOF. That's philosophy - not pure rule. And I didn't develop it - the coordinators did, so don't fuss at me, y'all.