As for price gouging, I'd prefer tax penalties tied to increases in gross margin that are, say, over 75% attributable to a price hike alone, similar to oil price windfall profits. More broadly, food prices, one of the two key worries for consumers, are also inelastic in many underserved areas, basically making grocery shopping like going to an expensive convenience store. This is best dealt with on a state level using zoning and tax policies to encourage better distribution. If, and I have no idea of the US case, the bulk of grocery shopping is dominated by only a handful of chains, breaking up monopolies by region can be a positive measure, medium term.
As for rent prices, however, there is a market dynamic in play of using housing now as any other traded asset on the stock market, leading to occasional false restriction of supply and overpricing. Again, monopoly legislation prohibiting any one group from owning a high share of housing in a given regional market seems the best measure.
On the political side, it has been decades since campaigns were run using well-designed, long-term policy. The remedy is political, and that involves breaking up media monopolies, such that competition in the marketplace of ideas becomes more a feature of campaigns. It would also help with the kind of misinformation that relies on repetition via multiple channels.