Speaking of what Palpatine wants, I also think Palpatine’s motivations need to be changed.
If Palpatine was Snoke, presumably, then Palpatine already knows that Kylo won’t kill Rey. And Kylo would also know that Palpatine knows that. If Palpatine as Snoke couldn’t get Kylo to kill her, then this guy Kylo just met definitely won’t. If Palpatine asked Kylo to bring Rey to him, it might be something more reasonable for him to ask. Then you could use Kylo’s masked dialogue to fill in that gap of why Palpatine wants him to bring Rey there. Maybe it is to kill her himself, maybe he tries to convince Kylo that he can help turn her to the dark side, or maybe he never tells him why and the truth is that he knows about the dyad and needs them both there to drain their power.
Whatever the reason, I think Kylo would look smarter if he knows it is probably a trap, and his goal is to find Rey and keep her from reaching Exegol, because he knows that is exactly what Palpatine wants.
EDIT: I suppose my motivation for this is that I still want to keep this idea that Kylo has overcome what Vader couldn’t to some extent. Vader was a pawn of the Emperor up until he threw him down that reactor shaft. I think Kylo Ren should stop being Palpatine’s pawn when he kills Snoke. So even though Palpatine is “alive”, Kylo sees past Palpatine’s machinations and tries to work against them. I think this would help keep Kylo’s character regressing too much from where we left him in TLJ.
Perhaps in the fanedit, you set up through the crawl that Snoke was one of Palpatine’s pawns or apprentices (Like Maul, Dooku and Vader) and now Kylo has destroyed his apprentice and impressed Palpatine. This way, Snoke isn’t a meat puppet and somewhat autonomous of Palpatine. You could still leave the line that Palpatine created Snoke, but now it is more metaphorical and just cut the vat of cloned Snokes. Also it solves the problem you were talking about, as Palpatine may not know exactly how Snoke was defeated in his throne room and Kylo’s conflicting feelings with Rey. It just seems a lot cleaner to me than Palpatine creating Snoke and literally controlling him.