Your solutions seem hacky and off-the-cuff, when we could solve the problem by addressing it directly: if a large number of people want to live in a small area, make that area support a large number of people! High-density housing with walkable neighborhoods, and excluding cars from walkable spaces, makes all of the typical pains of city-dweller life melt away.
Aside from a small group, the people that want to live there don't want that though. There's a preference for SFH and larger footage. It's generally easier to control commercial activity than personal activity/choice.
I see the real problem as too many people wanting to live in one spot. To me, my solution is addressing the root problem.
This is the exact problem. People do NOT, in general, want to live in high density housing, they want to live in these desirable areas without them changing.
There is simply no way to solve that equation without something breaking.