Swapping out a diff and replacing axles isn't that big a deal.
You might want to put it up on a lift in Neutral and rotate things to see if your drive shaft and U joints are all happy.
Is this the large case LSD with 8 bolt side plates? If your input bearing died, you could get a bit of play.
On an e30 we had the axle bolts fall out and the bang was heard when just one was left in and the axle shifted way off center.
It was a cheap fix as we had spare bolts and the car was just two blocks from home.