I actually think expanding the Supreme Court should be a long-term project: one new seat per presidential term, until the court has a total of 15 seats in 2044 (15 being a number I pulled out of my ass, just seems like a good size to me). That's a slow enough rollout that it can't be accused of one party stuffing the court, and it's fair because it gives several future presidents a say. Is that sufficiently 'non-politicized'?
Not that this kind of compromise would be acceptable to the other side anyway, they'll call foul no matter what because they're winning right now and won't accept anything that could potentially challenge that.