I just feel sad about one of the "base rules" of your mode : that there is NO remaining effect of the mythology after education. I love to have the beginning of my game having an effect latter.
The beginning of the game DOES have an effect later, in the same way that the vanilla game's early eras have effects later: the number of cities you have, the technologies you've researched, the improvements you've built, and so on all stay with you. What goes away are the direct effects, like how worshipping a Death god allows your units to rise from the grave after dying, or how worshipping an Animal god allows you to train mythological creatures. There are a few specific Foci whose effects are a bit more persistent. For instance, the Plants focus allows you to plant Forests and Jungles with its Myth units, and those obviously stick around after the Enlightenment.
Basically, the vanilla game's early eras were really only there to set up the board for the REAL part of the game; sure, a few civs will die during the Ancient or Classical, but the important part is the effect it has on the part stretching from the late Medieval to the end of the Industrial, when the most powerful nations will go on a conquering spree and/or build tons of Wonders. The key concept here is the "turning point", the one moment in the game when you realize that you've already won and that it's all just mopping up at that point. In the vanilla game, this point usually comes in the Industrial Era, and there's no point in playing through the Modern.
I wanted something that made the early eras important, but I also wanted to make sure that any significant advantages you gained in those eras didn't carry over to the later eras. You see, if they DID carry over, then there'd be no point in letting the mythological period end in the first place. The turning point would be even earlier than it was in the vanilla game, because whichever civs did best in the myth period would continue to dominate afterward. There'd be no point in even having those later eras; a game with this mod would become a game ONLY with this mod. So I CAN'T let a significant fraction of the effects persist, or else there'd be no point in using either of my other content mods with this one, because you'd never get to any of the content they add.
IN real life, the cultural aspects differences between greece and asia or mexico comprise some (many?) lingering aspects of their myth period.
What has stayed is what, in Civ5 terms, we'd call "Culture", as in, the pseudo-yield that unlocks Policies. The earlier religions DO still have effects on the modern-day culture, but those effects are very generic, not tied to the specific gods worshipped. (Besides, most of the cultures you mention don't even worship those old gods any more. Greeks don't still pray to Zeus, Mexicans don't pray to Tezcatlipoca, and most people have never even heard of the Sumerian gods.) While various parts of the modern societies might still identify with certain gods, you'd have a hard time convincing me that those gods have a practical impact that isn't attributable to the worshippers themselves; the Japanese corporations with shrines to Inari don't succeed because she's helped them out, they do so because they're selling their goods more often than the competition. At best, you'd assume they used the culture from that worship to invest in policies in the Commerce branch. Zeus doesn't throw lightning bolts at Greece's enemies, and Odin and Thor don't make Scandanavians unstoppable in battle. Obviously, the Hindu followers still actively worship their pantheon, but most of the others have long since been purely relegated to that "myth" status that makes them part of your culture (forming the basis of books, movies, etc. that keep people entertained) without any other effects.
This is mainly what the Piety branch in the Policies page already represents; the Happiness and Culture you get from the religious rituals themselves, but none of the effects that would be granted by the gods directly. And remember, you have to pick between that or Rationalism (the policy branch that adds research), so it's not like there's not precedent for my choice of making myth effects exclusive with the post-Myth period. And, the hidden policies I use to manage the Mythological Age already take this into account; ending the Mythological Age doesn't unilaterally reduce your benefits, you often get other things instead, mostly Culture, as the semi-religious content in the vanilla game shifts from being something you use to impress the gods to something that's just a part of your cultural heritage.
Take the Monument, for instance. In the vanilla game, it adds 2 Culture. During the Mythological Age it instead adds 1 Culture and 1/2/3 Favor. Completing the Enlightenment removes the policy, which changes it back to 2 Culture. In effect, then, you're gaining 1 extra Culture at the cost of the Favor. That is, you're no longer using that monument to impress the gods, you're now using it as a tourist attraction. Likewise, Stonehenge goes from 3 Culture and 3/6/9 Favor to 6 Culture; long after the druids stop using it for their rituals, it's still a notable part of the local culture. It's not always about Culture, either; a Colosseum gains Happiness at the cost of its Favor generation, as it transitions from "place for competitions honoring the gods" to "place for entertaining the public".
Maybe you can make it so there are some remaining effects of your early or later mythological choices; not something that would be overpowered, but some remaing effects
It's possible that I could give a weak remnant of some kind; I've toyed with this idea for a long time. For instance, if you worshipped Zeus in the mythological age, you might be left with a "Statue of Zeus" in your capital that acted like a National Wonder with weak effects related to Zeus' specialties and/or the Greek pantheon effects. Everyone would get one and only one, so the balance concern goes away. I'm not sure it's worth the amount of effort it'd take to implement this for 28 different gods, but it wouldn't be difficult to implement at all, as I've already got a Lua event that triggers on completion of the Enlightenment.
But again, powerwise these'd be fairly weak compared to the pre-Enlightenment effects, only at the level of a National Wonder. Basically, I'd just take the two Shrine bonuses for your primary and secondary Foci and add them together (unless you had one of the Foci whose effects are Myth-related, in which case I'll try to come up with something appropriate), plus throw on a small bit for the Pantheon. Nothing huge, but still something worth having.
Maybe you could make it that basillicas is not removed but transformed into a "ruins of X" in the city.
or
The place where the Tier IV mythological units are "rumored" to have died/lived
During the Enlightenment, you're given a one-time infusion of Culture and Golden Age progress for every religious building that downgrades (and it happens per downgrade, which means a Basilica gives you four of them as it goes down the chain). This is supposed to represent that sort of scavenging for other purposes, although its real point is to give you a sudden rush of policies and yields as you go through the Enlightenment, to make ending the mythological age a key time in your civilization. (Also, it helps offset the large penalties of the Mythological Age during a time when you're no longer getting the offsetting bonuses. I'm also looking at having the policies downgrade at the same time to keep this manageable.)
Likewise, you're given gold and science for every mythological unit that is disbanded. Maybe you killed that Minotaur and now have its head mounted on your wall, maybe you dissected that Hydra to see how it worked. The reason for this was to give players a rush of techs as they went through the Enlightenment, of course.
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Bottom line, I'm not completely opposed to having something persist. But whatever persists would have to be something that wouldn't magnify the power imbalances created during the Myth Age, and that eliminates a lot of possibilities.
