Is it possible for a habitable earth-like planet [364 day cycle, circumference 25,200 miles], to have three moons, the largest with 13 full moons a year, the next in size with 4 full moons a year, and the smallest and closest being nearly tidally lock and not visible to a third of the planet for 7,500 years at a time, due to that moon nearly having orbital synchronicity with the planet's 24 hour long full axial rotation?
All information with the exception of that relating to to the third moon comes from source material not produced by me so that it is put that way to be accurate - I saw some questions. Where I have not provided information you feel you need just assume the planet is otherwise pretty much identical to Earth except its axial tilt is currently 30 degrees not 23 degrees and continental land-masses will have different distribution. The planet is hollow but can be assumed to have same gravity as Earth.
To give context the world is a published setting that is meant to have a third moon although the published setting history produced for it relating to one segment of the planet going back more than 6,000 years omits making any mention of this. The only explanation for this I can see is it has never been seen by a sizable chunk of the inhabitants, in order to be recorded yet. Ironically most of that population has done its slow colonisation of the planet moving in the same direction the moon would be moving without any maintenance of records from where they originally came in the west
My question really is get at whether or not this omission of the third moon from the material can be accounted for by lunar behaviour capable of eluding detection by recorded memory for that time span assuming the moon reaches the zenith over any point on the planet once every 25,200 years. The moon is essentially moving slightly faster than the planetary rotation so it sits constantly in the sky but travels West to East over time but not noticeably so. It is close to reaching zenith at a point roughly 7,000 miles East from the periphery of the area for where the published setting history is documented.