I don't think they should have gotten rid of Dooku at all, but they should have kept Maul as a centric antagonist. The way I see it, there could have been a Triumvirate villain scenario present in the movies. You introduce Maul as the face of evil for both the Republic and the Jedi; many resources are dedicated by both to try and catch and defeat him, while war begins to boil under the surface.
Dooku leaves the Jedi after loosing faith in their ability to find and stop this Dark side villain, who ALSO killed his friend Qui-Gon. He is contacted by Sidious for his political savvy and resources and convinces Dooku to join him and Maul in reforming the Republic and Jedi. There is tension between Maul and Dooku, but Dooku is never officially made Sith and his plan-as was implied, at least to me, in Episode 2-is to instead start this war and convince Jedi that their order and the Republic need that change he is fighting for, WITH the ultimate plan being to betray the Sith in the end.
The Republic Senate, with their resources being dedicated to find Maul, has certain systems become disillusioned with the Republics function, and are convinced by Dooku that breaking away would be in those systems best interests. Those that remain are still given Maul as a centric enemy to keep the war in perspective as to "who's elimination would end it." If you need to think of a real life equivalent, think of Bin Laden to the US over the last decade. This only adds to their fear and want to give Palpatine power so he can better find and eliminate the threat then they have over the previous decade before Episode 2.
You could even have a mock relationship of Master and Apprentice set up between Maul and Dooku. At the end of Episode 1 they weren't exactly sure whether Maul was in charge or not, and the absence of a greater enemy than Maul could dupe the Jedi into believing they knew both their targets.
So in short: Maul is a galactic enemy and weapon of the Separatists, Dooku is the political mastermind behind engineering the war(at least to the public), and Sidious is pulling all the strings. Honestly, I think it gives you the opportunity to make Maul more menacing and Dooku a more interesting story, WHILE putting even more cards in Sidious' hands. Thus making the Prequel Trilogy better.