they were born probably shortly before, during, or shortly after the war... I believe in Serenity that they spoke about how just before the war there was a call for settlers to go out to Miranda - which is of course where the reavers were created.
and you could have more than 2 factions - you could start it out even earlier than the Alliance vs Independence war, before the core worlds began forming the Alliance, you could have different factions of Core worlds and Rim worlds, all vying for supremacy, with the eventual winners of the Core worlds forming the Alliance to their tastes, and the Rim worlds throwing their differences aside and forming a coalition which eventually gives way to the Independence movement.
If anyone wants help brainstorming for story ideas on a mod I would be more than happy to help