I'd simply start a progressive wealth tax at a high enough threshold so that a person could provide themselves with a reasonable nest egg. Pulling numbers out of the air, maybe 1%/year for the first $10 million, up to 10%/year for $100 million. (Note that if you live in a house, you're already paying some wealth tax). This would leave most people with both good and poor standing with enough to live comfortably, and the ones who got there by working will probably continue to make more to cover the tax.
Reducing inequality would hopefully have the benefit of aligning political goals with the interests of the population, in which case politicians would be more motivated to score things such as universal health care, workplace safety, education, a safety net, and so forth.
If the government were to be burdened by too much money, they could give some of it back to the poor. ;-)