Don't think of the background light as just a background light. Play with it. If you double the distance you will diminish the fallout.  You will need to double the output, and probably put a card so you don't spill light to your subject.  But play with the light, cut a cardboard in diferent shapes.  From diferent angles  Put a difuse before the cardboard, remove the difuser, move the distance to the screen, to the cardboard, the angle. You can also construct a snoot just wraping cardboard arround your flash head. Take a time to shoot not your portrait, but to shoot just backgrounds.