When I understand it correct, then here is one general error in this equation of time correction. The antikytera mechanism as well as the planetary clocks of the renaissance show the motion of sun and planets in the ecliptic plane. There the sun has a simple excentricity because only the variable apparent speed of the sun onto the ecliptic needs to be corrected. The second correction you do, is the obligity of the ecliptic. This component is only important, if you make a model which shows motions in relation to the celestial equator. The motion of the celestial sphere in geocentric astronomy is constant but the celestial day has a length of about 24 ×365/366