I've got it! One of the few things I remember from calculus over sixty years ago is: "Always examine the means and the extremes."
Suppose the earth's orbit were a perfect circle, and you were able to turn the sun into a huge stroboscope, that flashed only once in twenty four hours, and had it synch'd so the blip hit on the Greenwich meridian vertically.
If you could instantly on Jan 1 turn earth's orbit into an ellipse that shortened earth's distance from the sun, the blip would arrive early.
Isn't that easy to understand?