As it happens, living in the Bay Area I'm very aware of living in a house that, I could neither afford to 'buy' again, nor pay the taxes on should my prop 13 bill revert to 'current value'. But the way the tax base evolves in California is when property turns over or is sold. So when buy a house the taxing level is reset to the current value.
My suggestion is that by normalizing the tax burden to new owners without special "non-resident" perks, you would force the cost of ownership to be the same for everyone, and that would both discourage some rich folk from moving (lowering demand a bit and helping) and increase the tax base even though the number of residents was not increasing (which increases per capita services budget).
Now the last time I looked at buying a flat in Chelsea part of the thing that confused the heck out of me was the whole 99 year lease thing. I decided that real estate in London was going to need a lot more research than I had time for. A pity though because in 2002 when I was looking at it, I could have made a nice return.