I think this happens because we always store your velocity when walking as a horizontal velocity only, so when you transition to falling you are getting an initial horizontal velocity. You can work around this by hooking in to the “OnWalkingOffLedge” event and setting velocity to the result of “GetPhysicsLinearVelocity()” from the Character capsule.
You may only want to do this when moving downward, otherwise you may find that you start launching in the air when running off upward slopes (unless that it something you want).
Thanks for the image, that helped see what was going on quite easily 
-Zak