I admit I got your comment a bit confused with another talking about local government. But the solution I think is in the same direction - start local. The few hundred people in congress aren't self-sufficient. They need support from the rest of the party machines to get campaign money and turn money into votes. Changing what the parties will support at the local level changes who gets the big money and who gets elected.

Shorter version though: campaign finance reform, oppose voter suppression, and ranked-choice voting.