The methods are correct for both RET and FET distances to the sun. If the earth is round, one distance is computed to get the Round Earth value and if the earth is flat another distance is computed to get the Flat Earth value, using the same method. It's not a matter of an incorrect method -- it's a matter of an incorrect model.
Nope. FET distance measurement techniques are just wrong. Rowbotham can't use trigonometry correctly in EnaG. The Wiki entry uses only two latitudes and just ignores the other possibilities that provide inconsistent results.
Also if you're using the wrong model, you're using the wrong method.
Show us your calculation for the distance to the sun on the equinox from 20
o N and 50
o S please. Why don't you get the same value?