Given the high saturation of Jedi at many times in the history of that Jedi far, far away, I wonder if it might be better to *force* every player-character into the role and actually build the gameplay around it. We like to think of Jedi as special and rare, but translating this into actual, cohesive gameplay never really works. Setting this during the thousands-of-years-ago part of the Old Republic's existances gives you a convienient handwave to do away with that. Considering the population density of the galaxy, every player could realistically be an individual Jedi compared to all the NPCs who aren't Force-Sensitive.
There's another idea; if not make everyone a Jedi, make everyone Force-Sensitive. Jedi is one direction you can take it.
That line from the Incredibles fits the Jedi-in-games problem perfectly: I say they run with it instead of trying to bullshit new and flabbergastingly dumb ways of sidestepping it.
NOT THE BEES! NOT THE BEES THEY'RE IN MY EYES