Elections are the source of this problem; if you want working class people in government, you have to fundamentally change how politicians are chosen. The Athenian democracy did not have elections to the extent that we do. Athenians distrusted election because it almost always hands power to the rich. The real solution is to forego elections in favor of random selection of officeholders.
I've though about demarchy and I'm iffy. But at the very least make elections as democratic as possible--no campaign spending allowed whatsoever and ensure that officeholders can be recalled by their constituents at any time, and in general bring in Nix's proposals.