The question you've asked can only be answered on opinion and individual observation. Even If you were to look at every existing original car that still retained it's original carburetor you would only be seeing a very small sampling of what was originally built. Therefore there really is no "normal" that can be referenced with solid data, the dates are all over the map (in my own observation).
Here are some things to consider:
Chrysler did not have a "Fist in first out" inventory control program, they ordered carburetors (and other parts) from vendors who delivered them in batches, and used them until depleted in no certain order. This means a carburetor delivered to production inventory in June could just as easily been put on a car the very first day of production as the last during that production model year. Also consider that different carburetor manufacturers delivered at different frequencies, quantities, and locations based on the plants they supplied which affected the span of time between being made and arriving on the assembly line. Also consider that the more unusual the option/application (like a California car with a 383 and a fresh air hood for example), the longer it might have sat on the shelf waiting to put on a car.
So, bottom line, IMO, the June build carb in your application is 100% acceptable (and should be considered correct by ANY knowledgable judging program as such).