Tim,
No - I do not read/see 1960 specified in anything you posted. If I am wrong, someone will post a correction.
3739716 - was used from 1958 through 1962 on all truck 235 engines and some car 235 engines.
From 1958-1962, the Engine Serial Number was not useful in IDing the year-date of an engine, because same codes were used in several years. and no year information was in the ESN.
F 0361A - F 1203J
The A & the J at the end of the ESN is a model code.
The model codes were often the same in 1958-1962 years.
The A model code was used for a car engine 235 engine from 1958-1962.
As I posted above, if you want to know the year, you will have to find/post the Date Casting Codes for the head and the block.
The locations of date codes are shown here. Here is a page with links to serial numbers/codes for many years cars/trucks. Here is a page with casting codes for many years cars/trucks.