My diff is doing exactly the same and with the same amount of oil also
i think mine must be the front bearing seal that has gone/leaking, i wolud have thought the only cure would be to replace the seal but i would have thought that would big job involving undoing the main nut posibly alltering the bearing preload which i suposed to very difficult to reset.
if the leak is only minor like mine i would sugest just keep a eye on the oil level every now and again and top when nessarary,
as for cleaning try some GUNK engine degreaser and a stiff brush or even a soak with some penertrating fliud and a jet wash that should shift the oil.