Egyptians in the New World?

[Jona Lendering]

is there any reason that i could use as an excuse for a medium-sized fleet to travel far enough from the moroccan coast to be dragged off by the current?

You can imagine the governor of Tingitana, embarking upon an expedition to investigate the Moroccan coast, and discovering the Capeverdian Islands. That would not be impossible (cf. Agricola wintering on the Orkneys). Island hopping brings them to the west. One big storm, and you have a plausible scenario for ships being dragged off. In two weeks, you can be on one of the Leeward Islands.

I just don't think that Greek and Roman sailors were terrified of open water.

The Periplus of the Erythraean Sea describes the route to India. It includes a description of the trip from Aden, over open waters, to southern India (IIRC).