It's a good drawing but I went and double checked the class names (as I've never seen the nomenclature that you've been using before), and the only reference to any class name for the six CLGs in DANFS was one single line:
Springfield remained berthed at San Francisco until March 1959. At that time, she was towed from the west coast, via the Panama Canal, to Boston, Mass. On 15 May, she returned to the Fore River yard of the Bethlehem Steel Co. at Quincy, Mass., to be converted to a Providence-class Terrier guided-missile cruiser, and redesignated CLG-7
I think this fits with the conventional differentiation of the six ships into the Galveston Class (that had Talos) and the Providence class (that had Terrier). I'll recheck Friedman's but I'm fairly sure he uses the same nomenclature.
Edit: A quick check of the
Naval Vessel Register shows
Topeka as "CLG 6" class, which would be Providence.
Edit 2: The NVR entries for
Springfield and
Providence list them as "CG 6" class while
Little Rock and
Oklahoma City are listed as "CG 4" class. If I were to speculate the reason that the last two are not referenced as "CG 3" class is because
Galveston (
referenced as CLG 3) was struck prior to the 1975 realignment. This would still tend toward the use of simply the "Galveston" and "Providence" classes - IE differentiation based on the type of missile, not the presence of command spaces.