You really think that just because something is mentioned in the movie and has no evidence refuting it, doesn’t mean it’s automatically true? A fact is a fact. There’s nothing contradicting Kylo’s intentions to kill Palps.
And Palps wants to be killed, so Kylo saying he wants to kill Palpatine doesn’t tell us he’s doing anything against Palpatine’s plans at all, saying he wants to stop him would clear up any confusion on whether he’s on Palpy’s side or not.
Yeah, to me, the throne = power. Kylo doesn’t want to be a Sith, but he wants that power.
The issue I have with that is that Kylo just spent the last movie working to take a throne that represents power, introducing another throne that represents power that Kylo wants to take just feels like a regression. And like Jar Jar said this is called the Sith throne, so more than power it represents a legacy that TLJ Kylo wouldn’t have any interest in, it makes more sense that he’s looking to make his own throne stronger so to speak, rather than trying to take a new one.
As for the crawl, I agree with changing “attacking” to “silencing”, other than that I don’t think it should be changed. I think it’s better to keep whether or not Kylo’s really on Palpy’s side ambiguous until he reveals his true plans to Rey (rather than saying “he sees him as a threat!” from the beggining), and instead focus on the “threat to his rule” being the flames of rebellion ignited by Luke… “see you around kid”.