I agree the solution is not easy (or maybe even possible?).
I don't think paragraph two is possible. I think you can reasonably ignore numbers and just look at percentiles. It really doesn't matter how much the minimum wage earner makes, they will likely never be able to afford to buy a dwelling. The only scenario that lets them buy is if they climb on top of other people like government assistance, fixed income, etc. Say minimum wage went to 100K, "starter" home prices and rent would rise to meet the new ability to pay and fixed income renters would be driven to Porcupine to try to survive as they are still stuck at the pre-inflation income. I don't know what the actual percentiles are but I would guess something like the bottom 10% struggle to afford food and a place to live, the next 40% or so can survive rent or saving but not both (if they got lucky or help to get into the market they may be ok long-term), the next 20% can buy homes but will be house poor, the next 20% can buy an "affordable" house with little pain or step up in the market and be cash-strapped, the top 10% can do almost whatever the f they want. Changing minimum wage just changes who is in the lower percentiles, you still have the same number of people in each percentile.
I still think the best approach to housing prices is massive increases in supply. If a buyer or renter has a choice of 10 different properties that are reasonably equal, the properties try to compete on price and that helps those trying to find a place to live.