With proper dubbing, anytime "Grievous" is said, the mouth movement could also be adequately matched to "Vader" - give the General a makeover with a Vader Mask, that could be the swap.

My question - is there any way that the battle from the beginning of Revenge of the Sith could be moved to later in the film, so Dooku gets killed a lot later, showing Palpatine's influence growing?

I always felt that Revenge of the Sith worked better if Anakin DOESN'T kill the Sand People in Attack of the Clones. Just have his mom die in his arms, bring her back, have Anakin rant about wanting to be a better Jedi to Padme. Giving him some level of self control makes his fall more powerful later on. Otherwise, it isn't really a fall at all, but a realization of a flaw that was OBVIOUS and makes everyone around him look stupid.