Earlier quoted context omitted.
I've never seen a good solution for this. If the taxes get locked in, then you get the "2 neighbors with near identical houses paying totally different amounts in taxes" problem. If the taxes are not locked in, then you get the retired lifelong home-owner (or renter) on a fixed income, unable to afford the increasing taxes (or rents).
That is easy, eliminate property taxes. That property was bought with money that was already taxed. If you provide services, ask them to pay for the actual services provided, not for a generic tax. Common services like police can be split to the number of residents.
The reason property taxes are based on value is that it acts to tax wealthier people at a higher rate than poorer people. Plus, just because the money that purchased the land was taxed means nothing to the local community. Sure, the federal & state governments have already taxed that income, but that means nothing to the local community, who has to pay for schools and EMS every year. And these services act to make the property more valuable, so why shouldn't the residents of the community pay for them?