Ron from Florida
Allow me to clear up what appears to be confusing you.
The tapered barrel model lost the fourth screw in 1962 with the advent of the Model 10-4. Shortly thereafter, the 10-5 appeared with the change to the front sight width. This version also had the tapered barrel.
At the same time, the Model 10-6 appeared, which was the first three screw version with the heavy barrel (upgrade from the 10-3).
From 1962 until the end of 1976, the Models 10-5 and 10-6 were made concurrently, the former with the tapered barrel and the latter with the heavy barrel. So a 1963 serial number could be carried by either model. The same pairing was carried through on the 10-7 and 10-8, lasting until 1988.