This was inspired by @SirKeksalot 's post about matoran religion. This is how I would treat G3’s backstory.
"In the time before time, eight elements existed. they were separate, and warlike, the most barbaric being Light and Shadow. The other elements, Earth, Stone, Water, Air, Fire and Ice, wished to end this war. As such, they appealed to the Great Beings. The Great Beings granted their request for peace in the form of three brothers- Mata-Nui, Ekimu, and Makuta. These brothers each blessed the elements with a virtue- Destiny, Unity, and Duty respectively. Each also wore a Kanohi mask of power upon their face- Mata-Nui, the mask of Life- Ekimu, the mask of Time- and Makuta, the mask of Death. With these powers, Mata-Nui gave the elements creatures with destinies to inhabit them. Ekimu united the elements into Okoto, the land upon which we stand today, and gave it times and seasons. Makuta gave the land and its inhabitants duties to perform, and rest at the end of life. The three brothers also banished Light and Shadow from the land, to end the warring. however, before their banishment, however, they pled to the brothers that one would be allowed to stay. The brothers heard their plea, and gave a prophecy- ‘both will be allowed one champion, one Toa, to enter Okoto at a certain time. The two Toa would be mortal enemies, and fight for many years. Eventually, one will win the battle, and his element will be allowed to exist without banishment.’ So began the enmity between Light and Shadow.
"We, the Matoran on this Island, were given powerless Kanohi, but before Mata-Nui, Ekimu, and Makuta left Okoto, they gave two Matoran, Karzahni, and Artahka, two great Kanohi- Karzahni, the mask of Control, and Artahka, the mask of Creation. They used the powers of these masks to forge more Kanohi- masks that could not be wielded by we Matoran, but by ones far greater than ourselves- Toa. For, the brothers had prophesied that a Toa of each element would appear before those of Light and Shadow, to protect the Matoran from their war. For, while each element was pitiful compared to Light and Shadow, united they would stand a chance. Unfortunately, Karzahni became envious of his brother, Artahka. Karzahni decided to brake a sacred law and forged all of the powers of the Kanohi into one mask- the mask of Ultimate Power. With the mask at his side, he rallied the Matoran of Ice, Stone, and Air behind him, in an effort to revolt against the three brothers. Artahka sided with the other three elements- Fire, Earth, and Water- to war against him. In the end, he won, but at a great loss. His Kanohi was destroyed in the final battle. As tribute for his bravery, the brothers gave him back his mask renewed, and was granted his own realm of splendor and joy to rule, named after him. It was said that Matoran who led good lives according the three virtues would come to live there after their mortal lives were ended by Makuta. However, Karzahni would not go unpunished- he was given his own realm, also named for him, but it was a realm of misery and terror. It was there that bad Matoran would go after dying.
“Now, the age of the Toa has arrived, meaning that the battle of Light and Shadow is soon upon us. That is not all the Toa and us must worry about, however. Beasts of Karzahni- Evil Rahi, and Bohrok- have been terrorizing Okoto. Also, Matoran who live among us have began to follow Karzahni himself, calling themselves ‘The Brotherhood of Makuta’, because they believe it is their Duty to merge Okoto and Karzahni, banishing Artahka forever.”
(Basically, Makuta is Karzahni, and Mata-Nui is Artahka, but they have a similar backstory to Makuta and Ekimu. Oh, and I forgot to mention that the Toa of Light is Takanuva, and the Toa of Shadow is Umarak.)