Being a somewhat remote Morgan owner I've only really been exposed to my '75 4 seater ..... but my understanding is that the scuttle profile is taller and the windscreen deeper than the equivalent 2 seater ... though this is 'given knowledge' and I haven't made any definitive measurements myself so would not claim certainty.
The assumption does tie in with the 'wooden frame and skin' and 'bonnet each side' entries in the above list as a taller scuttle profile would require a taller bonnet side.
If you persue the project I for one would be interested to hear your definitive conclusions on the differences.
I started a thread called 'Morgan Specials' to see what was out there in the way of modifications ... there's been a few over the years but not the 4 to 2 seater you're considering (tho the guy mentioned above appears to have got at least past the woodwork stage from the pic on his thread)
Keep us informed if you can as it sounds an interesting project.
K