Difference-in-Differences setup for policy evalution
I think a DiD will not work here as the parallel trend assumption probably doesn't hold in your case.
However, given that the treatment is based on a number of parameters that are (I assume) observed, you could potentially use some type of discontinuity design to estimate the effect of the policy around the threshold values of these parameters.
To be more precise, your treatment neighbourhoods would be the the neighbourhoods that have the sign but are very close to loosing it, while the control neighbourhoods would be the neighbourhoods that are just below the threshold for obtaining the sign. Then if prices increases are a continuous function of all other covariates, the difference in treatment vs control would measure the effect of the signs for neighbourhoods around the threshold.
Of course there are potential endogeneity issues that you'll need to take into account as you can expect neighbourhoods to do some effort to get above the threshold.