If we want fewer wealthy white senators

then we should push harder for public funding of senatorial elections.

There's not many middle class or poor people who can take two years off from work to run for the Senate.

Maybe some kind of stipend for potential candidates who look like they have the energy and skills to pull off a successful campaign. That could be arranged through any number of pro-Democrat organizations (along with training to make them better public speakers, etc.)

Then public funding kicking in later in the process, whether the primaries or the general election.