Something, though that maybe ought to be considered is why is Maul being kept around if he is alive? Unless you are editing out the whole bit about only being two sith lords at once, wouldn't Maul be a threat to Dooku's position and therefore rivals? I don't know if one can work it in, but imply that Dooku has no idea who Grevious really is, and when Grevious talks to Sidious after Dooku is killed, Grevious is glad to have his rival gone and he thinks he has been restored to the position of sith apprentice, not knowing he is still just being used.
Something, though that maybe ought to be considered is why is Maul being kept around if he is alive? Unless you are editing out the whole bit about only being two sith lords at once, wouldn't Maul be a threat to Dooku's position and therefore rivals? I don't know if one can work it in, but imply that Dooku has no idea who Grevious really is, and when Grevious talks to Sidious after Dooku is killed, Grevious is glad to have his rival gone and he thinks he has been restored to the position of sith apprentice, not knowing he is still just being used.