I'd remove the connection to Sidious myself.

I'd have Dooku know all about Sith Sidious and be against him (through people like Gunray who were duped by him) and have him convinced he is someone high up in the Republic.

The Jedi come to think Dooku himself is the Sith Lord.

As for giving Obi-Wan a pupil I already suggested a solution there (I'm sure there are other ways of doing it).

Obi-Wan in episode one isn't Qui-Gon's student.

He is a fully trained Jedi Knight paired with Qui-Gon for a private investigation into the Naboo affair.

That way when Obi-Wan is adamant that he be allowed to train Anakin the line about already having a student is transfered to him instead of Qui-Gon.

That kid who played young Boba would be an ideal choice.

He could be trained by someone else (Dooku?) and Obi-Wan could train Anakin.