Nathan
Put your query to Hermen Pol on the FaceBook page "Morgan History Info" He has access to a lot of the factory records.
From my less educated perspective I would say that the bustle back was produced between 1953 (end of the flat rads) and 1957/8 when the classical "High Line" body came along. The bustle back was only used on the 2 seaters of course which again cuts down the potential numbers.
Having a chassis number makes your task a lot easier, I am sure we can track down the exact history of your car given time.