Most Jewish communities have been frequent involuntary migrants (e.g. the goyim tried to kill us, so we moved). Yemen and India and perhaps Ethiopia have stayed in one place. North Africa had some disruptions. Europe was always a mess (that’s how you had German speaking Jews in Ukraine, and Spanish speaking Jews in the Balkans). What is now Iraq and Iran were fairly stable. But even a place with stability, you had constant migration. And remember that living cultures tend to be constantly changing since that’s the way Ha-Shem programmed humans – if you constancy, stick to dead things.
If you really want to reenact life in the time Amoraim (late Classical and early Dark Ages, using the European perspective), consider getting a time machine.