Unfortunately for your analogy, the development of separate religious orders often happens more in the form of discrete events, like the Great Schism between Catholicism and Orthodoxy. In addition, systems of polytheism did not become, but were supplanted by those of monotheism.

Monotheism is far older than you may think – Pharoah Akhenaten in Egypt apparently attempted to expunge all deities besides Aten in the mid-14th Century BCE, but this change was quickly reversed after his death. However, more modern concepts of deism in particular are as old as pre-Socratic Greece.

The philosopher Xenophanes, writing in the late 500s and early 400s BCE, published works in which a mainly naturalistic (albeit scientifically incorrect) explanation for the universe nonetheless revolves around a 'god of the gaps', with an eternal prime mover at the centre – what Tim Whitmarsh in Battling the Gods refers to as 'deity-max'. This is by no means the origin of monotheistic religion, however. A crucial problem with this for ordinary Greeks was that this god could not be worshipped. How do you appeal to total abstraction? In a sense, a number of both pre-Socratic and sophistic philosophers are not unlike pantheists, using 'divinity' as an effective synonym for 'nature' or 'the order of things'.

Remaining in the classical realm, there were rational attempts to explain the existence of religion. According to quotations and fragments from Philodemus' On Piety, the mid-4th Century pre-Socratic Democritus argued that people originally devised pantheons to ward off evil, creating gods as the perceived need to keep ills such as natural disasters away increased, whilst the late-4th Century sophist Prodicus argued that they created gods to keep positive events like bumper crops coming. The Sisyphus fragment, meanwhile, comes from a play in which a character claims that the gods were created in order to keep the masses in check (its authorship is unknown – some suggest the tragedian Euripides, who was highly critical of the Greek pantheon, but the more common attribution is to the Athenian dictator Critias, a student of Socrates). This goes some way as to explaining why polytheistic religions were more widely accepted in the classical era than monotheistic ones – it was easy to accommodate sudden changes, be they natural or geopolitical (such as the sudden Athenian adoption of the Thracian goddess Bendis, as noted in Plato's Republic.)

At the same time, one can understand why the Romans changed to Christianity despite this. If we go by the Sisyphus view, the advantages of imposing a central religion on a multi-ethnic, multi-linguistic and multi-cultural empire may have been seen to outweigh the disadvantages of having to overturn existing religions and becoming less accommodating of potential future additions. In addition, the centralised Roman world was arguably more stable than the fragmented states of classical Greece, and so there was somewhat of a greater spiritual need to secure an afterlife as well as have a good mortal life. Existing Greek cults like the Eleusinian Mysteries were also too fragmented to compete with Christianity, despite probably (if we go by, among other sources, Aristophanes Frogs) having that personal, afterlife-based focus.

Thus, in many ways ideas about monotheism have been bouncing around since the classical period, but the transition from polytheism to monotheism as the dominant European religious type can hardly be considered evolution. The Greek pantheistic ideas arguably had little effect on or influence from Abrahamic monotheism, as they originated from an increasingly naturalistic philosophical climate, and the Roman adoption of Christianity can be considered a geopolitical ploy based upon the merits of monotheism for large empires, not the inherent disadvantages of pantheons.