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.
Of course, only 10% of residents were eligible for selection, which seems to be oddly neglected here. It handed power to the rich, anyway.
