Honestly, the only alternative Rey background story that I think could work decently is that there is a prophesied Sith chosen one created by the dark side itself as Anakin was by the light. But the final movie in a saga is a weird place to introduce such an idea.
This reminds me of an idea I had back when the film first came about, something I thought was a missed opportunity with the idea of the dyad (beyond that it should have been introduced earlier):
Would the Force, inherently dual in nature, with the whole central conflict between Light and Dark being about bringing balance and discovering what both truly mean, really create a Chosen ONE, rather than a Chosen TWO?
The hubris of the Jedi Order (that Luke himself decries in TLJ) was to completely stamp out and ignore the Dark, the equivalent of sweeping it under the rug, leaving people like Anakin in a terrible place. The constant folly of the Dark Side is absolute greed, which can never be sustainable (capitalism anyone?).
While Anakin went to both Light and Dark extremes, and people like Revan have been able to walk the line (though it did cause him and the galaxy a looot of problems), when the idea of the dyad was introduced I felt something really special could have been done with the idea of the Chosen One, which also would have ameliorated this film lessening the impact of Anakin’s sacrifice. To create true balance, the Force would make a Chosen Two, someone in the Light who struggles with the Dark, and someone in the Dark who struggles with the Light.
This is helped by Kylo already being a really unique Dark Side character, in that he doesn’t seek power as much as he seeks identity, leading to his constant conflict: the Dark Side can’t give him belonging and love. The theatrical films never delved enough into Rey struggling with the Dark Side but the Hal and adjacent edits (e.g. Starlight and Rekindled) bring it out brilliantly: she shows how tempting and easy the Dark Side is for a new, powerful, driven Force user, especially someone who has to learn so much so quickly like Rey and is desperate to defend her new family, the only one she’s ever had.
This doesn’t really have any bearing on the edit but I just wanted to share some thoughts!
EDIT: I also just remembered something else that I thought could augment this idea: Yoda in ROTS says to Windu and Obi-Wan, as they discuss if Anakin is up to spying on Palpatine and Obi-Wan affirms he’s the Chosen One, “A prophecy that misread could have been.”
EDIT 2: I just remembered ANOTHER part of this idea, related to the dyad: it’s not even a Chosen Two, but a Chosen Two that are One, perhaps why the prophecy was misread.
There’s no real way to make the idea work in TROS even with clever AI voices, as Rey and Ben don’t defeat the Emperor together and Ben dies. It’s more of a rewrite thing. Always intrigued me though!