How does the sun move in your model? Which trajectory? How many fewer sunrises?
In the model Lad peddles, the sun and moon go in daily circles above a disk. The circles vary in size throughout the year, and the sun is more like a spotlight.
I think even in this model, over one circuмnavigation (going in a circle around the "north pole"), you either get one fewer or one more sunrise, depending on the direction.
This model still has
several problems. One is that it doesn't work for the times when the southern hemisphere has longer days.
See below, starting about 4:30. (He's rather abrupt in his criticisms, but a globe was settled science in the middle ages.)