I suspect the new class designations and renumbering actually happened at the same time, from the same "master plan".
Class designations prior to 1924 were weight based.
C-16s were originally class 60 (for 60,000 lbs)
C-17s, C-18s, and C-19s were class 70 (weight rounded to nearest 1000 lbs).
K-27s were originally class 125.
T-12s came from two classes class 45, and class 45 1/2. (don't know why the 1/2).
the 2-4-0, 2-6-0 and 4-4-0 classes along with the class 56 2-8-0s never got updated since all were out of service before the reorganization.
In old photos the class designation can be found on the firebox below the running board. An engine which would later be a C-16 would read "B-4-60" Indicating two pony wheels, 4 driving axles, and a weight of ~60,000 lbs.
enjoy,
Phil Hackman