The only way for the myths to make sense is to turn the gods into abstract energy beings that appears to different people in different ways which isn't how anyone believed the gods to actually be.
Or don’t try to use the “multiple choice options” thing for anything contemporary to the story.
One thing it’s easy to forget about is that the only reason for multiple choice mythology in the present is that we’re getting multiple recountings from different places and different times about things that occurred long ago.
Back in Athens c. 500 BC, your local peasant of the day wasn’t hearing five different versions of the story of Hercules; they heard the one official recounting of the local priesthood.
We only have a multiple choice version of the stories because we’ve also gotten recountings from Sparta, from 300 years earlier, from 600 years later, from syncretised translations into Latin, and the interpretations of different scholars across hundreds of years each reflecting the values of their age.
It’s sorta like taking texts about the nature of Medieval life written in 1700, 1970 and 2020 and saying there are multiple interpretations of what life was like then... whereas today in 2021 we are going to view the more recent scholarship as accurate and the stuff written back in the 1970’s as the misinformed product of its age (ex. interpretating medieval depictions of armor as being “Studded Leather” vs. today knowing now they were depictions of Brigandine).
So the way to apply this realistically to your setting is to only apply “multiple choice” to historical events (ex. Different versions of the creation story or origins of the gods or the gods who came before the present ones), not to the present day religion/cosmology.
If you want to add versimultude there add the “multiple choices” as past interpretations that are now seen as flawed by present scholarship (studded leather vs. brigandine) or dogma (ex. the Catholic view of sex pre- vs. post- Theology of the Body and Humane Vitae)... but make clear that there is one version that is actually considered true (even if the accepted version is actually false).
Another bit I find works well for the Apollo problem is declaring that the physical universe is a reflection of the spiritual truth. When you use telescopes to look at the moon you see a big ball of rock orbiting the planet that reflects light from the sun; but this is merely the physical expression of the spiritual world where the realm of dreams reflects the divine light of inspiration down upon mindkind in the form of dreams.
Then the theologians can get into all manner of arguments over the exact nature of those spiritual associations while still having a concrete answer for those who look with their eyes.
The above also works better if your mortals can’t just routinely hop into the spirit world to get those spiritual answers confirmed, just like we can’t hop up to Heaven and confirm whether the Jews, Catholics, Islam, one of the Protestant churches or none of the above have the right interpretations).