Now that I have an AI Palpatine voice, I’ve been thinking through the Palpatine / Kylo introduction scene and how it can be modified to further support the goals of the Palpatine+ edit. Here is the dialogue I’ve been mulling over (some of it I’ve previously showcased):

P: “At last. Snoke trained you well.”
K: “I killed Snoke. I’ll kill you.”
P: “My boy… I made Snoke. I have been every voice you have ever heard inside your head. I have learned to make a great many things… thanks to Skywalker. The First Order was just the beginning. I will give you so much more.”
K: “You’ll die first.”
P: “I have died before. Kill me, and my spirit will pass into you, as all the Sith live in me.”
K: “You’re a ghost, in a rotting clone. What could you, give me?”
P: “Everything. A new Empire. Manned by legions of clones. Bred for obedience. Awaiting a worthy heir. The galaxy will cower before the might of the Final Order. But only the strongest may claim it. Kill the girl. End the Jedi. And become what your grandfather Vader could not. You will rule all the galaxy as the new Emperor. But beware, she is not who you think she is.”
K: “Who is she?”
Palpatine smiles and the screen fades to black.
P: “Your rival.”

A few of the reasons for these suggested changes:

I would be fine with the hand on Exegol not having any dialogue over it if it didn’t factor into the plot. But seeing as how Kylo later references Rey’s father taking the Skywalker saber from Exegol, I believe this is due for an explanation so that a casual audience can more easily put the pieces together.
It prevents the misconception that Palpatine’s clones contain Skywalker DNA, or worse yet, that Rey’s father is somehow part Skywalker. I’m fine with Snoke being part Luke (blue eyes!), but I’d leave that up to the audience to decide. My point is that this new line creates the impression that Luke’s hand merely allowed for Palpatine to make breakthroughs in his research into cloning, not necessarily that all of his creations physically contain Skywalker DNA.
Under Poe’s new dialogue later on, it’s made clear that the Final Order was constructed during the time of the Empire - “a stockpile”. So why then does Palpatine originally say it “will soon be ready”? I think Ascendant was relying on the idea that the Dreadnought cannon modifications were what was being worked on, which works, but I’m still not sure that I buy something of this scale being possible without the resources of the Empire. Thus I figure Palpatine acknowledging the state of the galaxy (“flames of rebellion”) is a better fit here.
Palpatine’s two new lines at the end more organically set up the central change of Heirs to the Throne, although don’t spoil it outright. So this way when Kylo later says “Palpatine wants us to fight”, the audience doesn’t start wondering if they missed something. Instead, they start realizing what’s really going on and it feels like a payoff to the intro.