I think what I would do if I wanted to get as much sludge and crap out as possible would be to put two hoses in the fill hole. One hose connected to a pump and a container to drain the old fluid, and one with a funnel on it. First pump out everything you can get, then while still pumping, pour some cheap solvent such as MMO or kerosene in. Continually pump out as much as possible. Once you have got it reasonably clean, fill with the proper gear oil, pump out, fill again, pump out, etc. until the solvent is gone or sufficiently diluted as to not harm the diff in normal operation.