Can't really agree with that naming either, Artistocrats could be both mercantile as well as populists themselves, Julius Caesar and the Gracchus brothers came from distinguished noble linages while leading Optimates like Pompey and Cicero were both from Equastrian backgrounds.
Perhaps... It depend, in fact, what you call an aristocrat, because "mercantile aristocrats" would be close to an oxymoron according to political philosophers of that time. Remember that being an aristocrat do not exactly mean being patrician or an eupatrid. Being an aristocrat mean being one of the best men of the City (
aristoi and
optimates both mean "the best ones", as you know), not only skilled but also honest and benevolent, acting for the common wealth. Birth distinctions are something that go with corrupted oligarchies, while the most logical way to found Aristocrats is trough the election by suffrage.
Timocrats and Plutocrats would rather be those who could be more logically associated to a mercantile faction as they give much value to goods and money, which tend to make them favour their social class wealth over common wealth.
When designing factions, I feel that the sole kind of pertinent questions is "who were their political allies? who were their clients? who supported them? who were their political adversaries?...". So, it is clear that Caesar and Gracchi Brothers were of the populist faction, while Cicero was of the aristocratic one, not the reverse nor any other.
The thirty tyrants and their partisans might be imperials...
To represent social classes and birth lineage, POPs and character traits would be, in my humble opinion, way more pertinent than factions. G. Iulius Caesar would have a patrician trait, perhaps even a descend of Venus trait, like all Iulii, but would anyway join the popular faction.