Just a suggestion to return to the process of making the audience believe Anakin is dead.
I was thinking about not making Obi Wan kill Grievous and move the Grievous-Palpatine hologram scene towards the end of the movie. When Grievous says “But the loss of Count Dooku…”, it could be changed with “But the loss of Anakin Skywalker…” (taken from the beginning, aboard the separatist ship). And then Palpatine says what we know: “His death was a necessary loss. Soon I will have a new apprentice, one far more powerful”.
It could enhance the belief that Anakin is really dead, and that Darth Vader will be Palpy’s new apprentice. Of course you would have to make Grievous survive, but sill.