Note: Nothing in this answer should be taken as a criticism of the general idea of setting a story in a world where the geocentric model reflects reality. What this answer aims to show is that such a world is necessarily fantastical, and mundane physics cannot circumscribe the author's imagination. A world where a geocentric model reflects reality is not our world; anything can happen, and this should not make the story any less interesting.
The classical geocentric model as described in Ptolemy's Almagest (originally Mathēmatikē Syntaxis, Mathematical Arrangement) worked like this:
First motion: The entire heavens rotates around the center of the Earth, once every sidereal day (23 hours 56 minutes 4 seconds).
Second and third motions: Each planet (including the Sun and the Moon) revolves with an uniform motion on a circle called the epicycle, the center of which is carried on a great circles called the deferrent:
The center of the deferrent is a point called the eccentric, and does not coincide with the center of the Earth; like the entire heavens, it rotates around the center of the Earth once per sidereal day.
The center of the epicycle moves on the deferrent with constant angular speed as seen from a point called the equant, placed midway between the center of the Earth and the eccentric.
This model is able to represent the motion of the Sun and the planets with reasonable accurracy, well within the limits of the astronomical instruments used by the ancients.
That is, well within the limits of the instruments of the ancients, except for the Moon. To make the model predict the position of the Moon, Ptolemy had to introduce a third circle. And with this complication, Ptolemy's model described the position of the Moon with decent accuracy; but in the effort of tuning the model to predict the position of the Moon, he had to allow its distance from Earth to vary by a factor of 2 in the course of a month, which was very visibly not the case. This difficulty was immediately recognized and remained unsolved throughout the antiquity and the Middle Ages.
The only solution is to go all modern and allow the Moon to orbit the Earth on an elliptical orbit with constant areal speed, but then this makes its motion qualitatively different from the motion of the Sun.
Geocentric models cannot be really made to fit with all observational data, unless all physics goes over the window and the universe is really put together in geocentric fashion.