How would they fix it? Obviously they could make some really cool things for Republics, but with people already entrenched with classes they like, and guilds formed, etc., getting them to change is going to have to be more than look how sexy this Jedi Knight's new belt is...
How about some easier things:
If a faction has 5% fewer players online they get a 1% bonus to all stats/effects/abilities etc. If they have 10% fewer, this goes to 2%, continuing on until a 5 or 10% bonus... Or this could be bonuses to XP gains, or legacy gains, or credit gains, or mission success rates, commendation gains, or whatever... If legacy gets implemented and its something players desire, you could give a bonus to legacy gains for the under represented faction (meaning it might be desirable to have characters of both faction on your account), since the legacy crosses to both factions. Allow guilds to have a faction mirror guild. The guild leader creates an opposite faction guild and the guilds link to each other, allowing cross faction guild chat. They could share a guild bank (once guild banks are implemented), not sure of the ramifications of allowing items to freely cross the faction barrier. Could even allow characters in the linked guild to group for operations, WZ, etc....
Just throwing out some ideas, many may have ramifications or loopholes that need to be carefully considered. Consider this a brainstorming session.