Start combining ways maybe?
I'm no physicist, or even a scientist of any kind. Maybe we need to stop thinking in terms of a single solution and start combining all the ways we know about that can actually move a spacecraft. If you had this starshot thing, solarsailing, nuclear thermal rockets, EM drive, gravitation assist or 2(maybe idk), etc, all on one small unmanned spacecraft. Like a "best effort" attempt, that's gotta do something. Has anyone ever done the math on that?