The way they ought to do is is by having the government set not the mill rate but the amount of government revenue to be collected per capita, and then have the mill rate calculated from (revenue per capita x total number of residents) / (total value of all property in the jurisdiction) every year.

The premise being that if property values change city-wide, property taxes don't, because property tax revenue only changes if the city's population does -- and if population increases then it's usually associated with new construction, so as long as the newly constructed units have a similar value per-bedroom to the existing ones, the amount you pay in property taxes doesn't change then either.

"Forced out" meaning they choose to sell rather than spend their unearned windfall.

They could always borrow against their massively appreciated property, after all.