The problem is the input shaft is directly in front of the filling hole, trying to fill it too quickly means the oil hits the shaft, can’t drain into the diff fast enough and comes back out of the filling hole.
The whining could be coming from anywhere, diff, cv joints, wheelbearings, always difficult to diagnose without swapping parts
From what you say it does sound as if the flange seals have gone but might be unrelated to the noise!
mike