Maybe my 3D imagination is bad but maybe someone can explain what I miss here.
Perhaps because it makes sense to me, I am unable to figure out what your are missing. I'll give it a go anyway.
As the sun spirals around above a flat earth, the furthest north it ever gets is the Topic of Cancer, and only at the Summer (northern hemisphere) Solstice. On that day, the subsolar point traces a circle around the flat earth's disc following the Tropic of Cancer, and after that it traces ever expanding circles on its way to the equator at the fall equnox and eventually the Tropic of Capricorn on the Winter Solstice. The sub solar point is always at a single spot directly below the sun. The sun never moves further north than the Tropic of Cancer, and therefor neither does the sub solar point. Hope that helps?