I have been thinking about the Grand Ave. Project. I know it's expensive but the park really needs to cover the entire central area in between First and Temple. Not only would this make the park significantly bigger, it would also bring it all the way out to the street. This park could easily become and significant place for the city. Likewise, a park covering the freeway would be wonderful. I think the civic center park would be more formal while the park over the freeway would include ball fields and play grounds.
There are significant problems with the courthouse and the Hall of Administration. That has already been put on the table. I would think there would be similar problems with the law library and the hall of records. Both of these are also older buildings. I remember the Hall of Records being a pit years ago, I don't know what it is like today. The other lot that has a building would be the criminal courthouse. This would undoubtedly be expensive to replace.
None of these building meet the current standards for governmental buildings. The criminal courthouse isn't set back from the street like modern sensitive buildings are.
I wouldn't mind some of the space being used for some key offices. But the large "block" buildings cut off the park from the rest of the neighborhood.
I would propose building new structures, that comply with the current standards. Looking at Google Maps, there seems to be a lot of space still in the Civic Center (or Civic Center adjacent). I think these new buildings may have large setbacks with wide tree-lined sidewalks. There may be some retail in the bottom, but not the density that you would see in the other parts of downtown. It would also be great if some of the ground floor space of these buildings could be used for the "retail" government services. That way, people don't need to go up into these buildings to pick up their permits or whatever. For example, a new courthouse may have a filing office on the first floor that also opens onto the street so all the people just dropping off documents don't need to go deep into the courthouse. This will provide some street activity and would be more convenient for those who need simple services.
I imagine the district to include other office and residential buildings that also comply with the same types of zoning standards. These buildings would be boxy and set back significantly from the street. The sidewalks would be very wide and include large trees. They would have large lobby spaces, but also have a retail component (probably no government offices on the first floor though).
I imagine all of these buildings be relatively short (about the 150' level). The district would extend toward Little Tokyo, toward the historic core, and perhaps across the freeway toward Union Station (this would be contingent on a park or a better way to connect the two sides.).
I imagine it look something like this, but with much wider sidewalks, that have trees and some street furniture separating the roadway from the sidewalk.