Given that we're playing in the Cold War, and that we have people playing characters on both sides of the conflict, I think starting with a politically neutral situation where direct conflict between the Empire and Republic is currently not present would be a good place to start. This would give us an opportunity to do some cross-factional RP and allow people to participate with flexibility. 

To give an example of what I mean, my idea revolved around Lannik, Bothawui, and the Bothan colonies, which are in close proximity to each other and are presently independent. I imagine that neither the Republic nor the Empire want those worlds to become territory of the other. My idea revolved around the formation of an economic agreement/non-aggression pact among them, played out from the perspectives of the PCs aligned with the Republic and Empire, both of which are supervising the negotiations to ensure that the trade agreements do not favor the interests of one of the superpowers over the other. This kind of situation leaves plenty of room for intrigue and the development of a conflict as things progress.  

A similar idea could be applied to worlds along the Imperial-Republic border. Maybe local elections on a world are favoring secessionists, or, seeing as Star Wars has a penchant for monarchies in the setting, the heir to a throne is particularly partial to the other faction and may lead his world to secede upon inheritance. 

Corellia could be an active counterweight to this, giving people looking to participate an active conflict a place to play, or, if we wanted to disregard Corellia in Flames, we could begin the RP earlier, in the weeks leading up to the revolution as things are put into play. 

I'm not sure how broadly appealing these ideas are, but that would be my preferred approach.