> but it needs to be done in such a way that it doesn’t fuck over existing property owners

This is impossible. The current system is such an extreme and unsustainable transfer of wealth towards property owners that there's no way to create a sustainable (let alone equitable) system that doesn't involve current property owners giving something up.

End Prop 13 protections for all property purchases. Stop grandfathering in existing property when it's inherited. It'll really fuck over new buyers in the short-term. But it's one way to get less resistance from existing owners - who are largely voters. And the skyrocketing property taxes on new purchases might put a damper on prices.

One of the main reasons behind Proposition 13 was to constrain rapid growth of local government expenses, and it has been effective in that. We do need to reform it so that the tax burden is distributed more fairly, but I won't vote for ending it without some guarantees on limiting government spending.

How do places without something like Prop 13 constrain the rapid growth of local government expenses?

Why is limiting government expenditure a goal in and of itself? If the government is able to raise enough tax money to support that spending, and voters agree with it, why shouldn't the government spend more?