To clarify, your car was scheduled for 3/1 and shipped 3/10, not delivered 3/10.
1967 Barracuda was a first year a-body, unavailable until late in the model year, and first year for a big block.
Imo, one could order whatever was on the menu, but on a first run of a new car, you're not getting the big block until they get some product out the door.
Iirc, manufacturers historically have delayed options, convertibles, etc.
All the current evidence shows all known 67 383 cars were scheduled to begin production on 3/1.
Find someone who works at Chrysler Historical and ask them to look at all the IBM cards, find all the Barracudas, and all the H code cars.
It would be interesting to see the casting date on your engine as well as the engine pad assembly date stamp.