If you're looking for a way to get rid of the canon characters (which I would highly recommend), there's already a convenient plot device to do that without having to go back in time. Use one of the timelines where they didn't succeed in killing the Beast and all died. Or say they all died after a different point and use that as your jumping off period.
I would go modern, or a few years into the future only.
I'm gonna go one step ahead and say don't base your game in Brakebills. The interesting part about the Magicians wasn't the magic university, it was Fillory.