My solution would be to start by introducing short-term parking meters at side-street parking spots. The meters would allow a person to buy time at a spot in chunks of 6-12 hours, at daily rates in the range of $2-$8/day with no time limit except that the car must be moved at street cleaning times.
In order to get over the hurdle of entitled resident parkers, we are going to work with the city and offer cheaper permits allowing free access only to those spots very close to their home, defined as no more than a few blocks surrounding their home address. The cost of such permits would only need to cover administrative costs. After collecting the money for a certain period of time, the plans of the parking garage will be a full go. With this garage, it not only benefits the people who live there, but for the people who work and shop in the area.