Given that during the Second Temple period, there were more Jews living elsewhere throughout the Roman Empire than there were living in Palestine, how were the requirements of Qorbanot fulfilled from great distances? I understand that vicarious presence at the Temple was provided by the system of Ma’amadot, but was there a similar system by which Jews in Rome or Alexandria could make sacrifices and offerings at the Temple?

I am unaware of any special provisions in ma'amodot for Jews living abroad. Preesumabely, the ma'amodot of Israel represented jews everywhere. Jews from abroad could send funds to purchase sacrifices and participate vicariously in the service. Apparently, there were Jews who travelled to Jerusalem for the three "regalim" (festvals), though it is doubtful if many came for all of them. Even a Jew living in Israel could send a sacrifice with an agent, so those outside the land could do so as well.