I also have a 65–3 that happens to be a 3” barrel. The Dash # on Smiths has nothing to do with barrel length.
All correct with one minor exception.The dash numbers represent engineering changes, NOT barrel length. Whatever you have been reading to suggest otherwise is completely wrong.
The serial number is ALWAYS stamped on the bottom of the grip frame. Many models (but not all) have the serial number stamped on the frame inside the yoke opening. The other numbers you may see inside the yoke area are assembly numbers to help keep fitted parts together at the factory.