T56X refers to:
T = Tonawanda engine assembly plant
56 = 1956
X = regular production 3100/3200 235 truck engine
The 56 would not have been used until 1956 but a 1956 engine might have been installed in a early 1957 truck.
3837004 (reference: Inliners) was used on 1955-57 235 truck blocks (Becks, shows this as 3738004, but I think that is an error). Do you have a reference for it being used on a 261 block?
You state: "I wonder how many motors have been changed due to lack of research." What does this relate/refer to? Engines being changed at a later date, out of convenience/necessity (when a replacement engine was needed)?
The original registration/titling might have been done based on the engine serial number (ie: BGCA) or by the vehicle serial serial number (cab-plate code), depending on the year, on the state, on the knowledge of the dealer/DMV when they first registered the truck.
Your truck has most likely had an engine swap (memories fail all of us over a 60 year period).
Does the valve cover have 4 machine screws on the sides or two bolt/nuts on the top?
There are other certifiably distinguishing characteristics between an original 1949 engine and the 1956 engine that you have. Are you able to post photos? We can request photos of specific engine parts, if you are interested.
One final consideration: I have an engine that has had the original engine serial number removed. Also, replacement Chevrolet engines might have come with no engine serial number. This would allow a shop/owner to stamp the replacement engine's bock with an engine serial number that would match title/registration.
