You can't legislate life into some gentle state. It is what it is. You can, however, smooth out the bumps.
Unfortunately, rent control does the exact opposite. It creates stupidity like this. Where a landlord has to use a lawyer to increase the rent 4X, which is insane on a number of levels. That is one hell of a bump in the road.
Get rid of rent control and prices will be stable. Yes, they will be higher for some, lower for others, but they'll be stable.