I believe that if the shadow path were charted accurately on a North Azimuthal projection it would take the shape of an arc, like the eclipse paths in Theodor von Oppolzer's North Azimuthal shadow path projections of the Solar Eclipse.
Above from
A Text-Book of Astronomy by George C. Comstock (p.113)
Fig. 36.—Central eclipses for the first two decades of the twentieth century. Oppolzer.
Future eclipses.—An eclipse map of a different kind is shown in Fig. 36, which represents the shadow paths of [pg. 114] all the central eclipses of the sun, visible during the period 1900-1918 A. D., in those parts of the earth north of the south temperate zone. Each continuous black line shows the path of the shadow in a total eclipse, from its beginning, at sunrise, at the western end of the line to its end, sunset, at the eastern end, the little circle near the middle of the line showing the place at which the eclipse was total at noon. The broken lines represent similar data for the annular eclipses. This map is one of a series prepared by the Austrian astronomer, Oppolzer, showing the path of every such eclipse from the year 1200 B. C. [pg. 115] to 2160 A. D., a period of more than three thousand years.
On a Flat Earth it is easy to see how a shadow arc could manifest upon a Flat Earth, with the Moon arcing below the altitude of the sun in three dimensions. Some additional clarification can be attained if the scheme of
Electromagnetic Acceleration is considered, where it is apparent that small movements of the Moon below the Sun, or of the Sun above the Moon, can magnify to larger effect.
I can see how the above could be possible in the Flat Earth model to create arcs in all of those areas. However, what is still curious to me is how this works in the Round Earth Model. In the Round Earth model how could the shadow path could arc Northwards like in the April 8th eclipse or in some of the Oppolzer eclipses in the above image if both the apparent Sun and Moon are traveling Westwards over the Earth's surface?
While the Moon's orbit in Round Earth Theory is not aligned with the plane of the Earth's orbit around the Sun, the misalignment is only at a 5 degree angle according to the official theory, and it is still curious how the shadow path can make such sharp Northward directions manifested upon the Earth.