Discussion here seems to neglect apsidal precession, also known as orbital or perihelion precession.Earth's axis precesses against the stars at a rate of one cycle per 25765 years, causing the well known precession of the equinoxes. This process is embedded within orbital precession. Due to movement of the whole orbit of the earth (apsides) with period of 112,000 years with respect to the background stars, earth's climate cycle has a period of about 21,600 years, the time it takes for the summer solstice to move from perihelion to perihelion, forming a main component of the Milankovitch climate cycle of glaciation.
The December solstice passed perihelion in 1296 AD. If axial precession were the only sort, then the solstice would return to perihelion after 25765 years. However, the perihelion is moving in the opposite direction against the stars from the solstice due to apsidal precession, making the period return of the solstice return shorter than the equinoctial precession. The perihelion has moved from the solstice about 12 days over the last 700 years, and now
occurs on about 3 January.