It would take a bit of digging, but I expect the answer is the Earth-Moon system mucks up the ellipse. The US Naval Observatory seems to take that effect (and the planets) into account. Basically, the Earth and Moon revolve around their "barycenter," their center of mass, and the barycenter traces the elliptical orbit. When the barycenter is at perihelion and the moon is away from the Earth (we see a full moon), the Earth is a little closer to the sun than if we had a new moon. Things are harder to visualize at other phases of the moon, but that's when the timing of perihelion seems odd.
Around 1980 I wrote a computer program to compute sunrise and sunset times with a thought about selling it through the OFA. My derivation was based on orbital mechanics ignoring planets and moon, but I needed a good reference time for perihelion. After figuring out the above I went to the library and looked through old OFAs looking for perihelions near full moons and that provide a decent reference. My program is still very accurate. Maybe for its 50th birthday I'll tweak some of my constants.
It would take a bit of digging, but I expect the answer is the Earth-Moon system mucks up the ellipse. The US Naval Observatory seems to take that effect (and the planets) into account. Basically, the Earth and Moon revolve around their "barycenter," their center of mass, and the barycenter traces the elliptical orbit. When the barycenter is at perihelion and the moon is away from the Earth (we see a full moon), the Earth is a little closer to the sun than if we had a new moon. Things are harder to visualize at other phases of the moon, but that's when the timing of perihelion seems odd.
Around 1980 I wrote a computer program to compute sunrise and sunset times with a thought about selling it through the OFA. My derivation was based on orbital mechanics ignoring planets and moon, but I needed a good reference time for perihelion. After figuring out the above I went to the library and looked through old OFAs looking for perihelions near full moons and that provide a decent reference. My program is still very accurate. Maybe for its 50th birthday I'll tweak some of my constants.