I assume you mean annual tax rate and if so you're making the same math mistake you made earlier. If they doubled over the last 10 years that means they went from ~$4k to $8k today, which is an increase of $4k over that period or approximately $333 a month. This would require about an $8k income increase over a 10 year period to cover it. A quick check says median household income in the bay area is ~$120,000, meaning the median household there would require a 0.65% annual raise to keep pace.
So even using your own numbers this is simply not a problem, definitely not a problem worth subsidizing people over. If you disagree I feel like you need to explain why a 0.65% annual income increase is an insurmountable obstacle.
This idea we need to shovel out massive subsidies to wealthy people so they don't move makes zero sense to me. How about instead we cancel those exact subsidies and put them into rental assistance, an area where stability is an actual problem.
If your house price has doubled since you bought it in any coastal metro area you have just made several hundred thousand dollars, tax free.
Right, I think this is common sense and basic fairness that if two people own identical properties they should have the same rights and obligations. No special treatment.