regardless of your diff free play, if your handbreak is ON you shouldnt be able to move either axle or move the car, so im taking a guess that you have a problem in one of your drums....
that said i'd also suggest that your S series center prolly does have some play... most do these days.
Im serious, handbreak on and i canturn the tailshaft roughly 2" in each direction. Although there is a slight pulse when i apply the brakes.
When the handbrake is on, the car doesnt move it just rocks (its the only way i can explain it) and there is a banging/knocking sound from out back.