The main method to connect the east and west coasts of East Africa is still through railways. Of course, connecting via waterways is not impossible, but it's definitely not something East Africa can achieve now.
That would mean networking the Zambezi River Basin and the Congo River Basin, which would require building a large number of hydraulic projects to improve navigation conditions between the two basins.
Such a project would be almost impossible to achieve even in the twenty-first century; just managing the Zambezi River Basin alone is incredibly challenging.
Of course, connecting these fragmented inland river waterways with railroads and highways wouldn't be too difficult for East Africa.
