My next article will be on this! I think the best way to go about it is a mix of more public housing and split-rate taxation. Given political constraints, I wouldn't mind replacing property taxes with LVT for the less well off in owner-occupied homes, while hitting everyone else with both. Still a lot of potential for revenue I think, between landlords and well-off owner-occupiers.

https://www.peoplespolicyproject.org/2018/01/26/how-to-handle-real-estate-with-a-social-wealth-fund/