I'm not a mechanical engineer, but the prospect of running the car without the axle halves in seems unwise. First, there's universal coupling that joins the axle half to the diff that would seem to be flapping around inside the axle tube, and that seems to me to be a really bad thing to do, and second, you'd be running it without oil. I assume you have the car supported on stands towards the outer ends of the axle tubes. If you run the car in gear with the axle tubes hanging down, you're bound to get some noise since the car isn't designed to operate at such an extreme angle.
Now that you've cracked the secret of getting the axle halves out, I would have thought that the next move is to replace the axle halves and seals, repack the bearings with the correct MB grease and reassemble having filled the diff with new oil (with the axle tubes level) and see how it runs then. I would have thought that the odds are in your favour that the problem has gone away. Worst case, you strip it again and go to the next level of fault finding. The only cost in this instance would be some oil and a bit of your time (and you could reuse the oil).