I don't understand why they would ever be getting closer to Earth. Wouldn't they be launched at a time of the year when Earth is moving in the direction the they are supposed to go in order to give them maximum speed?
http://solarsystem.nasa.gov/multimedia/display.cfm?IM_ID=214...
I believe the Voyagers didn't gain solar escape velocity at launch; they were sent to Jupiter via a regular Hohmann-like (half-ellipse) transfer orbit and used the gravity assist there to actually kick them to an escape trajectory.