My idea is that Jean in Uncanny X-Men 100-101 became a being of pure psionic energy, boosted by the solar flare, and became the original Phoenix. When Jean died on the moon in UXM #137, the Phoenix part of her, the core part of her psionic powers, survived as a separate entity. It started bonding with different creatures in order to survive and grew stronger, becoming a force on its own. It still needed to bond with other beings, however. It gained the knowledge and powers from beings it bonded with, growing ever stronger. And then one of them was a time traveller. The Phoenix force was now able to travel back in time, looking for its creator (Jean). It ended up in the Big Bang, gaining even more cosmic powers, and then we have the story told about its origin in Excalibur (at least I think that was where Big Bang was mentioned), that the Phoenix is one of the oldest beings in the universe.
Since it originated from Jean, before evolving into a separate being, this explains why it was attracted to the cavewoman, who resembles Jean. And why it always wants to return to Jean.
Since Jean had created a cocoon for her body to heal in, as a second chance, she has no first hand memory of how she was the true, original Phoenix. Yes, she has gotten its memories, but not before she was told what had happened, so the memories she got were influenced by what she was told.
It is not perfect by any means, but this would both keep the Phoenix force retcon as well as have Jean be the one, true original Phoenix.