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multiple relevant cycles
editI'm sceptical of some of the numbers and ancient astronomical motivations presented in this article. There are three relevant cycles: the tropical year, synodic lunations, and anomalistic months (more and less than 8 years).
(98 ~ 105 months) < (8 years) < (99 ~ 106 months)
2894 days = 7.9235 years = 98.0001 synodic lunations = 105.0280 anomalistic months < 2922 days = 8.0002 years = 98.9472 synodic lunations = 106.0442 anomalistic months
While there are 2 leap days and 3 leap months in 8 years (99 lunations), the phases most predictably repeat in slightly less than 8 years (98 lunations). This was known in Greece via Kidinnu in Babylon from before 350 BCE (251 synodic = 269 anomalistic months).