Doing the calculations at equinox is easy. You can even use the wiki to derive your data for the triangulation. Triangulation is required if you're using shadows or a sextant to calculate height.
To locate your latitude on the flat earth, it's important to know the following fact: The degrees of the earth's latitude are based upon the angle of the sun in the sky at noon equinox.
That's why 0° N/S sits on the equator where the sun is directly overhead, and why 90° N/S sits at the poles where the sun is at a right angle to the observer. At 45 North or South from the equator, the sun will sit at an angle 45° in the sky. The angle of the sun past zenith is our latitude.
Knowing that as you recede North or South from the equator at equinox, the sun will descend at a pace of one degree per 69.5 miles, we can even derive our distance from the equator based upon the position of the sun in the sky.
10*N Latitude, Distance from Equator=695 miles, Suns elevation 80*, Suns Height=3941 Miles
30*N Latitude, Distance from Equator=2085 miles, Suns elevation 60*, Suns Height=3611 Miles
45*N, Suns Height=3127 Miles
60*N, Suns Height=2047 Miles
80*N, Suns Height=980 Miles
So how was the suns height discerned to be 3000 miles?