Well, if I'm script-doctoring The Force Awakens, then I pull the old switcherooney and make Finn the force-sensitive grandson of Mace Windu. He's the one with the most interesting story anyway, so you might as well structure the sequels around him instead of Rey.
Rey's parents... I don't know. Maybe the interesting story isn't who her parents are, but who left her on Jakku. In that case, I would have altered the first movie's chronology to make it clear that there is something *really weird* about that planet. It's not a very well-known world, but people who do know it try not to stick around. And that crashed Star Destroyer Rey was scavenging looks like it's been there only a few years.
As it turns out, Jakku lies in a region of space where time passes slower. In the time that she's grown from a toddler to adulthood, the Galactic Empire rose, fell, and was reborn again in the First Order. She was a youngling being taken to the Jedi Temple when Order 66 was given, and the Jedi left her there with an acquaintance to keep her safe while he went to learn what happened. This is only hinted at in the first film, and confirmed in the second film.
In the second movie, while training with Luke Skywalker, Rey has Force-visions of the long-lost Jedi, and the acquaintance from Jakku who was supposed to watch over her. She sees the past and present, and sees that the Jedi had rescued something of great value and brought it to the desert planet for safekeeping.
Across the galaxy, guided by Snoke, Kylo Ren is having the same visions.
The third movie is a race to Jakku to find the woman who was supposed to raise Rey, but abandoned her and and pined for her lost friend. She is the link to the Jedi who returned to Jakku with a trove of records from the Jedi Temple, and just barely managed to hide them in a cave in the mountains before succumbing to his wounds.