OK - A little SPECULATION here.
First, let me state there is NO MENTION in any of the published Rochester documentation from the beginning in 1949 up through current offerings about a model C (other than the C meaning integral choke as mentioned earlier in this thread).
HOWEVER - In 1923, Carter Carburetor received its first MAJOR retail order from Chevrolet. At this time Carter did not have sufficient plant space to fill the order from Chevrolet, and Chevrolet was given license to produce Carter Carburetors in the Flint plant. Carter Carburetors produced by Chevrolet were identical to their Carter produced cousins EXCEPT numbered parts were numbered with the Chevrolet number rather than the Carter, and the castings carried a letter "C".
As GM owned Rochester, the Rochester B (unfortunately) became the standard 6 cylinder carburetor for Chevrolet in 1950, replacing the much superior Carter W-1. Possibly some other historian with actual data will jump in here; but I am SPECULATING that possibly history repeated itself, and these carburetors with the C were actually produced by Chevrolet. Repeat - SPECULATION ONLY AT THIS TIME.
Jon.