Keep the Senate the way it is, but elect Senators through proportional representation: each voter votes for a party, and that party gets as many Senate seats as its percentage vote share. Parties can choose the Senators they seat by any method that they officially publish before the election. This could be, for example, by having an internal election/primary that results in an ordered list, or even something strange like a rotating lineup of Senators, or the weekly winner of a contest.

People who cling to the Senate system because of the inordinate representation it gives to white, small states would happily give that up for the guarantee that they could get at least one neonazi Senator. We would have to deal with the fact that both Kim and Kanye would have a Senate seat, though.