Okay, I think I’ve figured out a way to reconcile these ideas about Rey and Palpatine, particularly with regards to Rey being some sort of vessel for Palpatine’s Sith spirit.
Going back a page or two, I suggested that Palpatine could have poured some of his power into Rey when she was a child, but as was pointed out this isn’t very Palpatine behavior. However, this could make sense if it was purely for the purpose of attaining immortality, explaining how he was able to cheat death in the first place.
We already want there to be a connection between what Palpatine created with Anakin and what he was planning with Rey. So maybe it’s a Harry Potter Horcrux situation, with Palpatine investing some of his life force into Anakin (and by extension his family) so that if he were to die, a part of himself could live on. He does the same thing with Rey once he comes back from the dead, since he is determined to destroy the Skywalker family who betrayed him. Thus he chose Rey, depositing some life force with her as well. Just like with Anakin, he knows that someday she will be important and so he plants this bit of himself so that even if he were to die at her hand, he could live on through her.
This is why Palpatine is in a crumbling clone body: he has given most of his life force to Rey and the Skywalkers, so he must gain that life force back from them if he is to be fully restored to life. And of course, this is what we see happen at the end of the film - he takes back what he gave them, reducing them in power while restoring himself. However, since he is now restored in this way, his insurance policy has been negated and he is mortal once more, even at the height of his power. This is why Rey is able to use his own power to destroy him, and why this death is final for ol’ Palpy.
Interestingly, this could also why Rey has the ability to give some of her life force to others - this is an ability that Palpatine discovered, and that she now uses for good.
The upshot of all of this is that neither Rey nor Anakin need to be created by Palpatine for this to work - merely that he has given some of himself to each of them at some point, presumably early in their lives, and this makes them powerful in the Force as well as naturally drawn to darkness.
Finally, this keeps Rey as a nobody born of nobodies while also being enough like Palpatine to be considered one herself.