I choose to insert Dooku in TPM's final moments because it's subtle, and because, to me, it works two ways: Mace's line and the pan hint at Palpatine being the master, and when Dooku shows up, it both creates some ambiguity

Subtility here is not far from confusion.

I think a "Palpatine or Dooku being the Sith Lord?" sub plot could work but, if so, I'd like it to be more obvious. I always found Dooku's character very poor on screen. Having a sub plot where the audience could wonder who, between Palpatine and him, is the Sith Lord could even add some interest in the political aspect of TPM. In other words I'd like to emphasis, in parallel, the dark side of both Palpatine and Dooku in TPM. (only that Dooku's is not yet a Sith, just a Jedi who don't like the council. He will turn to the dark side after the death of his only Jedi friend, Qui Gon.)

I think the audience needs to know even more obviously that the "phantom menace" is really hiding inside the Republic. The audience needs to know something the good guys don't. That's Hitchcock definition of suspens. Only here the audience also have a question in mind: Palpatine or Dooku?

EDIT: So showing Dooku having emotion at Qui Gon's funeral would be a way to tell the audience: Dooku is not a real bad guy (yet). So it has to be Palpatine.

Personally, why I don't like Dooku saying Obi-Wan should join him and help him destroy the Sith, is because it is a pretty big statement, that is never followed up on. Why does he say that? Does he really want to destroy the Sith? Or simply want Obi-Wan to join his cause? It seems like such a random line.

Kind of agreed. As much as I would like him to be the first leader of the rebels against Sidious, I know it would be hard to make an edit that follows that plot because of the small amount of footages we have.

Plus having him really turning to the dark side after the death of his apprentice (Qui Gon) is still quite an interesting character development IMO.