The most important problem is: How would you make a dynastic system work inside of a republic, while ensuring, that the game stays playable. CKII's republic system is far too simple to be implemented on Rome and a simple bribery system to get into offices would soon see the player having taken over the republic, actually denying the possibility to play as part of a republic.
Why would CK2's republic system be implemented in Rome when EU: Rome VV had a great Republic system already?
In any case, the player could just fight for multiple positions in the Republic/Monarchy, not just the government. Making family memebrs governors, generals, senators, etc. could make a good base I think.