A better threat, and probably one best done silently - is encroach northwards, and putting the effort in to irrigate (and drain in turn) vast swathes of land south of Khartoum (which would be a great site for a northern city even back then, especially one that is effectively the bastion against Egypt).
The draining of the Sudd generally works for creating new lands to farm (and with canals, high quality transport network is on hand), but irrigating south of Khartoum on an unseen scale could quietly, without much notice, cause the water levels to drop downstream. This could be done via both Niles, and if you wanted to go mental, you can connect both Niles via canals in expanding arcs south of Khartoum. Plus, doing it that way means that the dirt and rock removed for the canal can be used to create weirs and the like upstream, allowing the Ethiopians to force the water level up passively if needs be.
This could be used to effectively create vast lands to settle for Ethiopians long term, and my initial thoughts would be to have the PoD be the conquest of Soba much earlier than Yaqobs reign, and the founding/settling of a city of Ethiopians on the site of OTL Khartoum to strengthen the kings rule in the region. (I'd suggest a process of general urbanisation, but I don't fully understand Ethiopians problems with urbanisation historically to say).
But settling the region, and then slowly developing it using Nubian slaves, prisoners and general labourers is probably the way to go to have an expanded Ethiopia drain Egypts water supply.
(EDIT : I'd like to add that creating this vast potential agricultural region could very well FEED a rapidly urbanised Ethiopia, especially since they effectively have access to the water of the Nile, and its sediment to use as a topsoil replacement.)