If you figure that at every apogee they command a brief burst out of the station keeping jets to give AMC-14 a leeeeetle more momentum while at the same time moving it more towards 0? inclination, we should be seeing the perigee/apogee increase as the orbit "rounds" out.
A great thought experiment, really. The AMC-14 has a finite amount of propellant on board which will yield a given force when used. As the propellant is used, the satellite gets a little less massive, making it easier to accelerate. If the solar panels are fully deployed, the gyroscopes will be used to align the satellite for each maneuver, saving propellant. Each burn has to accomplish an increase in altitude, a decrease in eccentricity, and a reduction in inclination. Finally, the target location at 61.5?W has to be at or near the final maneuver or else you end up using more propellant to "slide" the satellite to the proper licensed position. Finally, you want to minimize the amount of propellant used to accomplish this to maximize the amount of time AMC-14 will have at 61.5?W. A compromise will be made in order to get AMC-14 to geostationary position as soon as possible, but without reducing the usable lifetime to too short of a time. Take too long to accomplish this, however, and you might as well launch a new satellite!
Phew!