You can probably go at least part of the way towards tweaking the leverage game by giving the President an FVRA-like power to, say, designate any A3-confirmed judge to serve as an acting justice once the seat has been vacant for N days after a nominee is sent up.
But it's hard to see how you could prevent a determined majority willing to accept that from trying to "steal" esp a 2nd term seat in hopes their party wins the WH. I guess you could eliminate seats that aren't filled within a Pres term, but that would still skew the numbers over time.